Connections on a Hypersurface in a Projectively Metric Space
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 160-170
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We study intrinsic geometry of hypersurfaces embedded into a projectively metric space $K_n$, $n\ge3$, and normalized in the sense of A. P. Norden and E. Cartan. We construct affine and projective connections on $V_{n-1}$ induced by normalizations of the indicated types and find conditions under which the induced connections are flat.
Keywords:
projectively metric space, duality, normalizations of a hypersurface, affinely connected space, projectively connected space, space of constant curvature.
@article{UZKU_2009_151_4_a12,
author = {A. V. Stolyarov},
title = {Connections on {a~Hypersurface} in {a~Projectively} {Metric} {Space}},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {160--170},
publisher = {mathdoc},
volume = {151},
number = {4},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a12/}
}
TY - JOUR AU - A. V. Stolyarov TI - Connections on a Hypersurface in a Projectively Metric Space JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2009 SP - 160 EP - 170 VL - 151 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a12/ LA - ru ID - UZKU_2009_151_4_a12 ER -
%0 Journal Article %A A. V. Stolyarov %T Connections on a Hypersurface in a Projectively Metric Space %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2009 %P 160-170 %V 151 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a12/ %G ru %F UZKU_2009_151_4_a12
A. V. Stolyarov. Connections on a Hypersurface in a Projectively Metric Space. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 160-170. http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a12/