SCIENTIFIC ABSTRACT LAPTEV, G.F. - LAPTEV, N.G.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000928620020-2
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 31, 2001
• Sequence Number: 20
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

F. DifferehW -geometry of i
MY. -%Ta mbeddtd maid-
4 did UnT -zeo-
eren 9
r"tric Ituristizado" Trudy, Moskov. Mat OW. 20~
As- the subiftld'of paper. indicates, the met-
inyestigAtionofsubspa isgrouktheoretic. For this reason
-itial prop-
the first part of the paper is a,m=6 of the esse.
ertiesof Ue ps. In particular the fundamental dif(er-
grou
-Cartan P and d
entiallionais.of efined. by
~re used to obtain the equations of Ui* This grouli G, of
r R.
ir alized b~ means of. an n-dimei*onal
parameters, is rei
Let H be
-a fixed subgroup of G .
~nAytic qwMin.ate *cc
zhaving no in Ivariant subgroup. in 'comnion With 6 (or U.'
And H 6ve a r6indmal i invariant subgroup P, one tak-ei'
'the factor groupsG/D, HID). This-subgroup-0 is the "group
of *uppore,, and has in in~age F in the 4W
rea on space,
ing s t n f* is thiw
e ta io ary- or. Y.. A geometrical object
b
i4opW as a pcilat in any i~e# ~ fict- space!S Of the irou~, of
opordinaes am referred to the coordinate
Support, Whose dew
ha b
Wanm of F. This aKr= wi r, E of Vej_en and
that the com-
~ad but itis constructive in the~sense
ponents. (coordinates ol.a: point in S) are givew as solutions
I- das~ It is in this
of qiftms of total Mempa equaO. m er
ttai ii~~fims of " Ire, .'affing rs, pseudo-tensors care
The last
constructed, two chapters are.devated to, the study
but beyon
lof Ahe geometril ~Jejcts of a subspaw, d the
miisfy,-tbe,,:
iiOD3,an itions must*
lg6eW r* that they.'
J

laptevo 0 F.-
-K
resulls&* aiiiier. Ordy in ft cW-of4be*qj6cfivo Fiffer...
:ential geometry of a surface is the work complete and all
Ithe classical invariants- are obtained frorn this general.
1principle. In'bonclusion, the authbr-Ptates that the methods"
!developed can be applied equally well to affine and con-,
_'formal geometry of subspacm, but that the algebraic diffi-~
leuWa litcom -a unresolvable, In the reviewer's opinion, the
imain ~-gue of this goup-theoretic method,is not so muchl
'as a trimns of 1n)mstigating any. particular geometry, but asi
.4 Ubifyink priftriple for all of n*Om differential geometry.
A S. Knewmax (Pullman, W~yh

L' 11 PTF V
-USSR/Hathematice- Mathematician FD-1181
Card 1/1 Pub. 118-22/30
Author t Laptev, 0.
Title Mathematical life in the USSR. Sergey Pavlovich Finikov, on his
70th birthday (16 November 1953)
Periodical Usp. mat. nauk, 9, No 3(61), 245-252, Jul-Sep 1954
Abstract All'of the investigations of S. P. Finikov relate to the field of
differential geometry, particularly the geometric configuration of
ordinary three-dimensional space, as shown in the list.of his,87
works (35 preliminary reports and notes, 1925-1954; 35 memoirs, 1912-
1951; 5 monographs, 1917-1950; 5 textbooks, 1932-1952; 8 popular
articles, 1927-1953). He presently holds the chair of differential
geometry in Moscow University and is an honorary member of and member
of directorate of the Moscow Mathematical Society. All his works are
noted for their simplicity and clarity of exposition. Some of his
students are: N. V. Laktanova, V. I. Korovin, T. A. Shullman, R. V.
Smirnov, T. L. Kozlmina,, V. T. Bazylev, I. N. Grigorlyev.
Institution
Submitted

AUTHOR: I 1p Lte ~vG ~ SOV/20-121-1-10/55
TITLE: Hypersurface in the Space of Projective Connection (Giperpoverkhnost,
v prostranstve proyektivnoy svyaznosti)
PERIODICAL: Doklady Akademii nauk SSSR, 1958, Vol 121, Nr 1, PP 41-44 (USSR)
ABSTRACT: The author constructs the differential geometry of the hyper-
surface in a multidimensional space of projective connection
with a curvature and a torsion. The author considers especially
the generalization of the notions of the projective differential
geometry of an ordinary surface. He uses a group theoretical
method. The reBults have an invariant character and are valid
.-in,the spaces of Riemann, Weyl and in spaces with an affine
connection. The obtained formulas are interpreted geometrically
by giving the geometric objects to which--t"y-norrespond in the
local spaces (Darboux-cone, linear element of Fabini, direction
cone of Pubini etc.)-
There are 3 references, 2 of which are Soviet,and 1 French.
ASSOCIATION:Moskovskiy gosudarstvannyy universitet imeni M.V.Lomonosova
(11oscow State University imeni M.V.Lomonoeov)
PRESENTEDt February 25, 1958t by P.S.Aleksandrov, Academician
SUBMITTED: February 11, 1958
1. Mathematics
Card 1/1

8
16(1)
AUTHOR: Laptev,G.F. s0-7120-126-3-8169
TITLE: - -rn-v-ariant Equipment Of a Surface in Affine-Connected Space
PERIODICAL: Boklady Akademii nauk SSSR,1959,Vol- 126,Nr 3,PP 490-493 (USSR)
A13STRACT: The problem of invariant eqiiipment of an n-dimensional surface
in an N-dimensional space of affine connection consists in the
determination of a field OIL (N-n)-dimensional planes (normals),
connected invariantly with the surface, each of which has only
one common point with the corresponding tangenting plans. in the
plane affine space the problem was considered by k.Ye.Liber
f-Ref 12 and P.I.Shveykin Z-Ref 22. In the present paper the
author considers the in7ariantl equipment of a surface in the
space of affine connection with ourvature and torsion; the
author restricts himself to the simpleat casez N