.

Теорія кривини грассманового образу підмноговидів в евклідовому і рімановому просторі: Автореф. дис… канд. фіз.-мат. наук / В.М. Савєльєв, Харк. дер

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OA?EIANUeEEE AeA?AEAAIEE OI?AA?NEOAO

NAA?EUe?A Aaea?ie Ieoaeeiae/

OAeE 514

OAI?Iss E?EAEIE A?ANNIAIIAIAI IA?ACO IIAeIIIAIAEAeIA

A AAEEIAeIAIIO I ??IAIIAIIO I?INOI?I

01.01.04 – aaiiao?iy i oiiieiaiy

Aaoi?aoa?ao

aeena?oaoei? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oiceei – iaoaiaoe/ieo iaoe

Oa?eia – 1999

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia a Oa?eianueeiio aea?aeaaiiio oiiaa?neoaoi I?i?noa?noaa
ina?oe Oe?a?ie.

Iaoeiaee ea?iaiee

aeieoi? oiceei-iaoaiaoe/ieo iaoe, i?ioani?

Aiiiia TH??e Aoiaoiae/,

i?ioani? eaoaae?e aaiiao??? Oa?e?anueeiai aea?aeaaiiai oi?aa?neoaoo

Ioioeieii iiiiaioe:

aeieoi? oiceei-iaoaiaoe/ieo iaoe, i?ioani? Aeineaio Aaeaioei ?aaiiae/,

i?ioani? eaoaae?e aeui? iaoaiaoeee *a?eanueeiai
?iaeaia?ii-oaoiieia?/iiai ?inoeoooo,

aeieoi? oiceei-iaoaiaoe/ieo iaoe, i?ioani? I?eea Aiaoie?e Aeieo?iae/ ,

i?ia?aeiee iaoeiaee ni?a?ia?oiee (O?ceei-oaoi?/iee ?inoeooo iecueeeo
oaiia?aoo? IAI Oe?a?ie, i. Oa?e?a)

I?iaiaeia onoaiiaa

?inoeooo iaoaiaoeee IAI Oe?a?ie, a?aeae?e oai??? iaaeeaeaiue ooieoe?e,
i. Ee?a

Caoeno aeena?oaoei? aiaeaoaeaoueny 17.09.1999 ?. i 15.00 aiaeeii

ia caniaeaiii niaoeiaeiciaaii? a/aii? ?aaee E 64.051.11 i?e
Oa?e?anueeiio aea?aeaaiiio oi?aa?neoao? ca aae?anith: 310077, i.
Oa?e?a. ie. Naiaiaee, 4, aoae. 6-48.

C aeena?oaoei?th iiaeia iciaeiieoenue o Oeaio?aeuei?e iaoeia?e
a?ae?ioaoe? Oa?e?anueeiai aea?aeaaiiai oi?aa?neoaoo ca aae?anith ie.
Naiaiaee, 4.

Aaoi?aoa?ao ?icineaiee 16.08.1999 ?.

A/aiee nae?aoa?

niaoeiaeiciaaii? a/aii? ?aaee
?aiaoiae/ N.TH.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Oaia aeena?oaoe?eii? ?iaioe a?aeiineoueny aei
oai??? a?anniaiiaiai ia?aco i?aeiiiaiaeae?a o aaee?aeiaiio i?inoi??, yea
?ioaineaii ?ic?iaey?oueny ia aeaiee /an.

Ieoaiiy, ui iia’ycai? c aea/aiiyi i?aeiiiaiaeae?a aaee?aeiaiai
i?inoi?o aeaaii aeceaathoue ?ioa?an o aaiiao??a. Aaiiao??y
i?aeiiiaiaeae?a ? /anoeiith no/anii? aaiiao???. Nii/aoeo, aaiiao??y
iiaeiiiaiaeaeia aoea o?eueee /anoeiith ??iaiiai? aaiiao???, aea
nueiaiaei? oea ? naiino?eiee iai?yiie a aaaaoiaei??iiio ocaaaeueiai?
eeane/ii? oai??? iiaa?oiiue. Aaiiao??y i?aeiiiaiaeae?a aea/a? iia?
oaeoe, ui ia iathoue aiaeia?a a eeane/i?e oai??? iiaa?oiiue. Aaiiao??y
i?aeiiiaiaeae?a iinoaaeea oa ?ica’ycaea iia? oe?eaa? i?iaeaie ?acii c
?? niaoe?aeueieie iaoiaeaie. Aiia ia? oaeiae aaaaoi yaieo oa
ianiiae?aaieo ca’yce?a c iaoai?eith oa o?ceeith.

Iiiyooy e?eaeie ? iaeiei ?c oeaio?aeueieo iiiyoue
aeeoa?aioe?aeueii? aaiiao???. Ca ae?acii a?aeiiiai o?aioeocueeiai
aaiiao?a Ia?naey Aa?aea e?eaeia ? “??iaiiaee ?iaa??aio ? 1”. E?eaeia
oaeiae a?a? aaaeeeao ?ieue a o?ceoe?. Iai?eeeaae, ?oo o?ea a
a?aa?oaoe?eiiio iie?, o a?aeiia?aeiino? c caaaeueiith oai???th
a?aeiiniino? Aeiooaeia, aecia/a?oueny e?eaeiith i?inoi?o-/ano.

Aeia?a a?aeiia oa ?ieue, yeo a eeane/i?e aeeoa?aioe?aeuei?e
aaiiao??? a?a? aaocniaa noa?e/ia a?aeia?aaeaiiy iiaa?oiiue. Aaonniaa
a?aeia?aaeaiiy, yea iaceaa?oueny oaeiae a?anniaiiaei, ciaeoei
canoinoaaiiy i a aaaaoiaeii?iie aeeoa?aioe?aeuei?e aaiiao???. Aiii
ie?aeii canoiniao?-oueny ye i?e aeiaaeueieo, oae ? i?e eieaeueieo
aeine?aeaeaiiyo i?inoi??a noaei? e?eaeie. Iniaeeai oni?oii aaonniaa
a?aeia?aaeaiiy canoiniao?oueny i?e aea/aii? aeaiaei??ieo iiaa?oiiue ?
aiia?iiaa?oiiue aaeeiaeiaiai i?inoi?o.

A?anniaiiaee ia?ac iiaeiiiaiaeaeo a aaeeiaeiaiio i?inoi?? ? eiai
aaaeeeaith aaiiao?e/iith oa?aeoa?enoeeith. Aea/aiiy a?anniaiiaiai ia?aco
i, a ca’yceo c oeei, aeine?aeaeaiiy aaiiao?e/ieo aeanoeainoae
iiiaiaeaeia A?anniaia a inoaii?e /an i?eaa?oa? ana a?eueoee ?ioa?an.

aai iiiiiaeueia, aai iaeneiaeueia.

.

Aeineiaeaeaiiy a?anniaiiaiai ia?aco iaeiiiaiaeaeia o aaeeiaeiaiio
i?inoi?i i?iaiaeeeinue a i?aoeyo Y.Muto , TH.A.Aiiiiaa ,,,, Ai?enaiei
I.A., Iieiea?anueeiai TH.A. , oa iioeo. Ieie iaea?aeaii ?yae oai?ai i?i
e?eaeio a?anniaiiaiai iiiaiaeaeo aeey ieiuaaeie, aeioe/ieo aei
a?anniaiiaiai ia?aco. ?acoeueoaoe, yei iaea?aeaii aei 1989 ?ieo
aenaioeaii a iaeyaeiaie noaooi Ai?enaiei I.A,Iieiea?aneee TH.A. 9. A ,
?icaeyaeaeenue aaonnia? a?aeia?aaeaiiy i?aeiiiaiaeae?a o ??iaiiaeo
i?inoi?ao noaei? e?eaeie. N.A.Eiceia cai?iiiioaaa eiino?oeoe?th
noa?e/ieo a?aeia?aaeaiue o aeia?eueiiio ??iaiiaiio i?inoi??. Ia/eneaii
oi?io iao?ee noa?e/ieo a?aeia?aaeaiue oa ?icaeyiooi ?yae ne?aenoa.
Iaea?aeaii oi?io iao?eee noa?e/iiai a?aeia?aaeaiiy, ui, ca oiiae
noaeino? naeoe?eii? e?eaeie ia?aoai?th?oueny o a?aeiio oi?ioeo Iaaoa. Ia
iiaa?oi? aaaaeaii aeayeo eaaae?aoe/io oi?io, iacaaio oi?iith
o?eaei??iiai ne?ooa. Oey oi?ioea ia? aiaeia aeey iiaa?oi? .

; yeui aeeeth/-ieo i?i?iaeueieo iiaa?oiiue c iaia?.

? ae?oaa ooiaeaiaioaeueia oi?ia .

. Aieiaiee ?acoeueoao ?iaioe ? ne?aeoth/a

a.

? a?anniaiiaei ia?a-cii ?aaoey?iiai o?eaei??iiai iiaeiiiaiaeaeo
(m+3)-aeii?iiai aaee?-aeiaiai i?inoi?o.

naiiai iii-aiaeaeo A?anniaia acaeiaae aeaiaeii?ieo ieiuaaeie, aeioe/ieo
aei a?ann-iaiiaiai ia?aco (yea ye aaea aiaecia/aeinue aeua ).

. Oi?ioea, ui aaniina?aaeiuei ae?aaea? e?eaeio /a?ac eiaoioei?ioe ,
iaaaaeaia TH. A. Aiiiiaui a 4. Aiaeiioeii oaeiae, ui iiaeiaio oi?ioeo
?aiioa cono?i/a?ii o E.Iooi 3 .

(a oe?e oi/oe?), ? oi/eiaa eiaei??i?noue i?aeiiiaiaeaeo a oi/oe?
(?ici??i?noue ia?oiai ii?iaeueiiai i?inoi?o) aei??aith? 1.
TH.A.I?eiea?anueeei aoea aeiaaaeaia

) i?aeiiiaiaeae c iaae?iaeaeaiiei a?anniaiiaei ia?acii, i?e/iio
?ici??i?noue n oa eiaei??i?noue m caaeiaieueiythoue iaei?e c o?ueio
oiia:

;

;

3. .

Oiae?

a) A eiaei?e oi/oe? ?nio? aeioe/ia ieiuaaeea aei a?anniaiiaiai ia?aco,
acaeiaae yei? e?eaeia iiiaiaeaeo A?anniaia ia a?eueoa 1. sseui a ye?enue
oi/oe? iaeiaioa cia/aiiy e?eaeie ii an?i ieiuaaeeai ? 1, oi e?eaeia ii
an?i ieiuaaeeai aei??aith? 1.

b) A inoaiueiio aeiaaeeo i?aeiiiaiaeae ia? oi/eiao eiaei??i?noue 1 ?,
yeui oea aeeiiaii o an?o oi/eao: ? a?ia?iiaa?oiath.

Ine?eueee caaea/a ? “oi/eiaoth”, oi a aeiaaeeo eiaei??iino? ie ia
iaea?aeo?i i?/iai iiaiai o ii??aiyi? c aeiaaeeii . Ioaea, iica
?icaeyaeo caeeoeeinue eeoa ne?i/aiia /enei aeiaaee?a. A oie aea /an aei
i?eiouaiiy 2) TH.A.Iieiea?anueeei aoa iiaoaeiaaiee eiio? i?eeeaae i?e
n=4, m=3. Iaaeae? aiai?y/e i?i aiiioaco I.A.Ai?enaiea ie aoaeaii iaoe ia
oaaci i?eiouaiiy ioieoa 1).

aea/a?oueny o aeaio iai?yieao: 1) aioo??oiy aaiiao??y a?anniaiiaiai
ia?aco; 2) ciai?oiy aaiiao??y a?anniaiiaiai ia?aco. Iaiao?aeii
a?ae-i?oeoe, ui an? ?iaioe iia’ycai? c ia?oei iai?yieii i?enay/ai?
aea-/aiith a?anniaiiaiai ia?aco oe?eeii aecia/aieo eean?a
i?aeiiiaiaeae?a.

?c iaaaaeaiiai iaeyaeo noaio ieoaiiy aeaeii, ui ?yae iaae??oaieo
ieoaiue ua iio?aaothoue naiai aeine?aeaeaiiy. Cie?aia oeieaaei ?
ieoaiiy i?i e?eaeio 2-aei??ieo ieiuei aeioe/ieo aei a?anniaiiaiai ia?aco
iiaeiiiaiaeaeia, yei iathoue iaaii aaiiao?e/ii aeanoeainoi aai
iiaeiiiaiaeaeia, ui iathoue iaaii a?oie ?ooo.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, oaiaie. ?iaioa
aeei-ioaaeanue ai?iaeiaae 1993-1999 ?.?. ?ie?a ca ieaiiaith oaiith
eaoaae?e aaiiao??? Oa?uee?anueeiai aea?aeaaiiai oi?aa?neoaoo “A?anniai?a
ia?ac” aea?aeaaiee ?aa?no? ? 0187004404 .

Iaoa ?iaioe. OeIaoith iaoiai aeine?aeaeaiiy ?

1) aeiaaaeaiiy a?iioace I.A.Ai?enaiei;

.

.

Iaea?aeai? ne?aeoth/? ?acoeueoaoe aeena?oaoe?? ? iiaeie.

) ;

. E??i oiai anoaiiaeaii aeeiiaiiy a?iioace a eean?
eiiieaenii-aiae?oe/ieo iiaa?oiiue.

3) aia?oa aeaia oa?aeoa?enoeea aeayeeo niaoeiaeueieo eeania
iiaeiiiai-aeaeia a oa?iiiao e?eaeie a?anniaiiaiai ia?aco;

4) anoaiiaeaia oi?ioea aeey ii?iaeueii? e?eaeie a?anniaiiaiai
ia?aco i?aeiiiaiaeaeo a aaee?aeiaiio i?inoi??. C’yniaaii, ui oey e?eaeia
iiaea ?i\caeyaeaoenue ye aiaeia ne?ooa e?eai?.

c ieineith ii?iaeueiith ca’yci?noth oa anoaiieaii, ui ?ciia?aiao?e/iee
i?aeiiiaiaeae ia? noaeo aioo??oith e?eaeio.

I?aeoe/ia oa oai?aoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a.
Aeine?aeaeaiiy iiaeooue aooe aeioe?eueieie i?e oai?aoe/iiio ?icaeyae?
aaiiao??? i?aeiiiaiaeae?a. Iaoa?iaee ?iaioe iiaeooue aooe oaeiae
aeei?e-noaii aeey /eoaiiy niaoeiaeueieo eo?nia nooaeaioai, yei
niaoeiaeicothoueny ii aaiiao?i?.

Iniaenoee aianie caeiaoaa/a. Ani ?acoeueoaoe yei aeeeaaeaii o
aeena?oaoei?, iaea?aeaii aaoi?ii naiinoieii.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. ?acoeueoaoe aeena?oaoei?
aeiiia?-aeaeenue oa iaaiai?thaaeenue ia Oa?eianeiio iinoeaaiio naiiia?i
(ea?ia-iee – aeaae. I.A.Iiai?aeia), ia naiiia?i eaoaae?? aaiiao?i? OAO
(ea?iaiee /eai-ei? IAI Oe?a?ie Ai?enaiei I.A), ia nai?ia?? “aaiiao??y ?
oiiieia?y ” ( ea??aiee – i?io. TH. A. Ai?iia), ia I?aeia?iaei?e
eiioa?aioe?? ii aaiiao??? a oe?eiio (i. *a?eane –1995 ?.).

Ioae?eaoe??. Ca oaiith aeena?oaoe?? iioae?eiaaii 3 noaoo? a
oaoiaeo aeaeaiiyo oa 1 oaca aeiiia?ae? iaoeiai? eiioa?aioe??.

No?oeoo?a ? ianya ?iaioe. Aeena?oaoeiy aeeeaaeaia ia 137
noi?ii-eao ? neeaaea?oueny c anooio, 3 aeaa, aeniiae?a oa nieneo
e?oa?aoo?e, ui ioiieth? 59 iaeiaioaaiue.

Aeaae iathoue ne?aeoth/? iacae:

Ae. 1. Iniiai? oi?ioee, oaeoe oa aecia/aiiy.

Ae. 2. I?i a?anniaiiaee ia?ac i?aeiiiaiaeae?a a aaee?aeiaiio
i?inoi?? o yeeo ei?ici??i?noue ia ia?aaeuo? ?ici??iino?.

.

CI?NO ?IAIOE

.

iiiaiaeaeo A?anniaia, aeey iai?yieia aeioe-/ieo aei a?anniaiiaiai
ia?aco aeaiiiai iiaeiiiaiaeaeo

.

E?ii oiai, a oeueiio ae ia?aa?aoi oi?ioea aeey naeoeieii? e?eaeie
a?anniaiiaiai ia?aco caienaia /a?ac e?eaeio ii?iaeueii? oa aeioe/ii?
ca’yciinoi caaeaiiiai iiaeiiiaiaeaeo:

,

iiaeiiiaiaeaeo. Oey oi?ioea ? iioa oi?ia aiaeiiai-aeiuei? oi?ioee ic 3
.

Ae?oaa aeaaa i?enay/aia ae?ioaiith aiiioace Ai?enaiei I. A. aeey
iiaeiiiaiaeaeia a aaeeiaeiaiio i?inoi?i o yeeo oi/eiaa ei?acii?iinoue ia
ia?aaeuo? ?icii?iinoue naiiai iiaeiiiaiaeaeo. Aeiaaaeaia

ia ia?aaeuo? 1.

. A ?oaioi 20 iieacaii, ui .

A ?iaioi 9 aoei noi?ioeueiaaia neiaeoth/a ieoaiiy: /e ai?ii, ui a
aeiaieueiiio o?eaeii?iiio iiaei?inoi?i, yeee ? aeioe/iei aei iiiaiaeaeo
A?anniaia, ? aeaiaeii?ia ieiuaaeea acaeiaae yei? naeoeieia e?eaeia ia
ia?aaeuo? 1? Neiaeoth/a oai?aia, aeiaaaeaiiy yei? iaaaaeaii a ia?aa?aoi
1 aeaae 2 aea? iiceoeaio aiaeiiiiaeue ia oea caieoaiiy.

.

yea i?oiaiiaeueii ia?aoeia?oueny c ainnth oa oeaio?ii ui eaaeeoue a
oeie ieiueii. Aiaeioe/ii aeiaieueiee iiiiiaeueiee eiiie/aoee
iiaeiiiaiaeae iiaea aooe iienaiei ?aaeion-aaeoi?ii

. Anoaiiaeaia

iaae aeaaa?ith iiaeaieieo /enae iaceaa?oueny iiaa?oiath ?iaiiai
iaoeeo, yeui o anio ?? oi/eao aeioe/ia ieiueia ieiueia i aieiaia
n-ieiueia icieeiiii, oiaoi ani ?o noaoeiiia?ii eooe ?iaii iiae niaith.
A i’yoiio ia?aa?aoi aeaae 2 aeineiaeaeo?oueny ca’ycie a?anniaiiaiai
ia?aco c aaiiao?e/ieie aeanoeainoyie iiaeiiiaiaeaeo.

.

acaeiaae aeiaieueiio ieiuaaeie yei i?ioiaeyoue /a?ac oeae iai?yiie,
ia ia?aaeuoaaea 1.

2n-2. Oaeei /eiii ia? iinoea

ia ia?aaeuo? 1.

Aeiaaaeaiiy oei?? iniiaii? oai?aie aeaii a ia?aa?aoi § 3.3.
Ineieueee i?e aeiaaaeaiii oei?e oai?aiu nooo?ai aeei?enoiaothoue
aaiiao?e/ii aeanoeainoi iiaeiiiaiaeaeia, oi a ia?oiio ia?aa?aoi
iaaaaeaii aeayei oaa?aeaeaiiy ic , ui noinothoueny iiiyooy ni?yaeaieo
iai?yieia.

ii. Oeae oaeo aeei?enoiao?oueny i?e aeiaaaeaiii iniiaii? oai?aie a
ia?aa?aoi § 3.3.

. Aiii aoei ?ica’ycaia Iooi oa I. A. Ai?enaiei, TH. A. I?eiea?anueeei
aiaeiiaiaeiuei.

c ieineith ii?iaeueiith ca’yciinooth iaceaa?oueny iciia?aiao?e/iei,
yeui ani eiai aieiaii e?eaeie ia?aeaeueii a ii?iaeueiie ca’yciicoi.
Aeyaey?oueny, ui aioo?ioiy e?eaeia a?anniaiiaiai ia?aco
iciia?aiao?e/iiai iiaeiiiaiaeaeo ? noaeith.

AENIIAEE

) aeey i?aeiiiaiaeae?a eiaei??iino? yea ia ia?aaeuo? ?ici??i?noue. Oeae
?acoeueoao ? iie?auaiiyi a?aeiia?aeiueiai ?acoeueoaoo
TH.A.I?eiea?anueeiai.

. E??i oiai anoaiiaeaii aeeiiaiiy a?iioace a eean?
eiiieaenii-aiae?oe/ieo iiaa?oiiue. Oeae ?acoeueoao ? oaeiae iie?auaiiyi
a?aeiia?aeiueiai ?acoeueoaoa TH.A.I?eiea?anueeiai.

3. Anoaiiaeaia oi?ioea aeey ii?iaeueii? e?eaeie a?anniaiiaiai
ia?aco i?aeiiiaiaeaeo a aaee?aeiaiio i?inoi??. C’yniaaii, ui oey
e?eaeia iiaea ?icaeyaeaoenue ye aiaeia ne?ooa e?eai?.

c ieineith ii?iaeueiith ca’yci?noth oa anoaiiaeaii, ui ?ciia?aiao?e/iee
i?aeiiiaiaeae ia? noaeo aioo??oith e?eaeio.

?iaioa iineoue oai?aoe/iee oa?aeoa?. Iaea?aeai? ?acoeueoaoe oa
?icae-

iai? a i?e iaoiaee iiaeooue aooe aeei?enoai? i?e aea/ai? aaiiao???
i?ae-

iiiaiaeae?a a aaee?aeiaiio i?inoi?? a oeo iaoeiaeo oa o/aiaeo cae?eao

aea aaaeaoueny aeine?aeaeaiiy i?aeiiiaiaeae?a a aaee?aeiaeo oa
iaaaee?aeiaeo

i?inoi?ao. Iaoa??aee, ui i?noeyoueny a aeena?oaoe??: iiaeooue
aeei?enoia-

oaaoenue oaeiae i?e /eoaii? niaoe?aeueieo eo?n?a c aeeoa?aioe?aeueii?
aai-iao??? a iaae?inoeoooao oa oi?aa?neoaoao.

Ia caaa?oaiiy aaoi? ue?i aeyeo? naiai iaoeiaiai ea??aieea
i?io.

Ai?iiaa TH.A. ca iinoaiiaeo caaea/ oa aeiiiiiao a ?iaio? iaae
aeena?oaoe??th.

NIENIE I?AOeUe IIOAE?EIAAIEO CA OAIITH AeENA?OAOe??

//Oe?. aaiiao?. ca. – 1992. – Aui. 35- p. 125–132.

2. Naaaeueaa A.I. E oai?ee e?eaeciu a?anniaiiaa ia?aco iiaeiiiai-ia?acee
a aaeeeaeiaii i?ino?ainoaa //Iao. oeceea, aiaeec, aaiiao?ey. – 1994. –
T.1,N3/4. – C. 520–528.

, ei?acia?iinoue eioi?uo ia i?aainoiaeeo ?acia?iinoe //Iao. oeceea,
aiaeec, aaiiao?ey. – 1998. – T.5,N 1/2. – C. 125–133.

4. Naaaeueaa A.I. I e?eaecia a?anniaiiaa ia?aca //Iaaeaeoia?iaeiay
eiioa?aioeey ii aaiiao?ee a oeaeii . *a?eanu, 1995. – N. 78 –79.

AIIOAOe??

Naa?eue?a A. I. Oai??y e?eaeie a?anniaiiaiai ia?aco i?aeiiiaiaeae?a
aaee?aeiaiai oa ??iaiiaiai i?inoi?o. – ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.01.04 – aaiiao??y ?
oiiieia?y. – Oa?e?anueeee aea?aeaaiee oi?aa?neoao, Oa?e?a, 1999.

-aei??iee aiaeia ne?ooa e?eai?. Aeaaaeaia oi?ioea aeey e?eaeie iao?eee
a?anniaiiaiai ia?aco i?aeiiiaiaeaeo c ieineith ii?iaeueiith ca’yci?noth.
Aeaii canoinoaaiiy oe??? oi?ioee aeey ?ciia?aiao?e/iiai i?aeiiiaiaeaeo.

Eeth/ia? neiaa: i?aeiiiaiaeae, iiiaiaeae A?anniaia, a?anniaiiaee ia?ac
i?aeiiiaiaeaeo a aaee?aeiaiio i?inoi??, naeoe?eia e?eaeia iiiai-aeaeo
A?anniaia acaeiae ieiueie aeioe/ii? aei a?anniaiiaiai ia?aco.

Naaaeueaa A.I. Oai?ey e?eaeciu a?anniaiiaa ia?aca
iiaeiiiai-ia?acey aaeeeaeiaa e ?eiaiiaa i?ino?ainoaa. – ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoa-iaoe/aneeo iaoe ii niaoeeaeueiinoe 01.01.04 – aaiiao?ey e
oiiieiaey. – Oa?ueeianeee ainoaea?noaaiiue oieaa?neoao, Oa?ueeia, 1999.

). Eiaao ianoi

ia i?aauoaao 1.

-ia?iue aiaeia e?o/aiey e?e-aie, a eiaiii aa?ia

oiaeaeanoaaiii ?aaiyeanue ioeth.

Auaaaeaia oi?ioea aeey e?eaeciu iao?eee a?annniaiiaa ia?aco
iiaeiiiaiia?acey n ieineie ii?iaeueiie nayciinoueth. Aeaii i?eiaia-iea
yoie oi?ioeu aeey eciia?aiao?e/aneiai iiaeiiiaiia?acey.

Eeth/aaua neiaa: iiaeiiiaiia?acea, iiiaiia?acea A?anniaia,
a?an-niaiia ia?ac iiaeiiiaiia?acey, naeoeeiiiay e?eaecia iiiaiia?acey
A?anniaia aaeieue ieiuaaeee eanaoaeueiie e a?anniaiiao ia?aco.

Savel’ev V.M. Theory curvature of the Grassmannian image of
submanifolds in Euclidean and Riemannian spaces. – Manuscript.

Thesis for candidate’s degree on speciality 01.01.04 – geometry
and topology. – The Kharkov State Universyty, Kharkov, 1999.

. The performing a hypothesis in the complex-analy4tical class of
surfaces is stated. The formula for the normal curvature of Grassmannian
image of submanifold in Euclidean space is also given. The fact that
this curvature can be considered as an analogue of torsion crooked is
showing. The formula for the curvature of metrics of Grassmannian image
of the submanifolds with flat normal conection. Aplication for this
formula for isoparametric submanifolds is given.

Key words: submanifolds, manifold Grassmann, Grassmannian image of
the submanifolds in Euclidean space, sectional curvature of the
Grassmann manifold in the tangent planes of the Grassmannian image.

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