FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 2, PAGES 103-114

**Internal geometry of hypersurfaces in projectively metric space**

A. V. Stolyarov

Abstract

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In this paper, we study the internal geometry of a hypersurface
$V$_{n-1} embedded in a
projectively metric space $K$_{n}, $n$³
3, and equipped with fields of geometric-objects
$\{Gi$_{n},G_{i}}
and $\{Hi$_{n},G_{i}}
in the sense of Norden and with a field of a geometric object
$\{Hi$_{n},H_{n}}
in the sense of Cartan.
For example, we have proved that the projective-connection
space $P$_{n-1,n-1} induced by the equipment of the
hypersurface $V$_{n-1} Ì
K_{n}, $n$³
3, in the sense of Cartan with the field of a
geometrical object $\{Hi$_{n},H_{n}}
is flat if and only if its normalization by the field of the object
$\{Hi$_{n},G_{i}}
in the tangent bundle induces a Riemannian space $R$_{n-1} of constant curvature $K\; =$-
1/c.

Location: http://mech.math.msu.su/~fpm/eng/k10/k102/k10211h.htm

Last modified: April 5, 2011