Centroaffine differential geometry and its relations to horizontal submanifolds

Luc Vrancken. "Centroaffine differential geometry and its relations to horizontal submanifolds." Banach Center Publications 57.1 (2002): 21-28. <http://eudml.org/doc/282229>.

@article{LucVrancken2002,
abstract = {We relate centroaffine immersions $f: Mⁿ → ℝ^\{n+1\}$ to horizontal immersions g of Mⁿ into $S^\{2n+1\}_\{n+1\}(1)$ or $H^\{2n+1\}_\{n\}(-1)$. We also show that f is an equiaffine sphere, i.e. the centroaffine normal is a constant multiple of the Blaschke normal, if and only if g is minimal.},
author = {Luc Vrancken},
journal = {Banach Center Publications},
keywords = {affine differential geometry; affine hyperspheres; product structures},
language = {eng},
number = {1},
pages = {21-28},
title = {Centroaffine differential geometry and its relations to horizontal submanifolds},
url = {http://eudml.org/doc/282229},
volume = {57},
year = {2002},
}

TY - JOUR
AU - Luc Vrancken
TI - Centroaffine differential geometry and its relations to horizontal submanifolds
JO - Banach Center Publications
PY - 2002
VL - 57
IS - 1
SP - 21
EP - 28
AB - We relate centroaffine immersions $f: Mⁿ → ℝ^{n+1}$ to horizontal immersions g of Mⁿ into $S^{2n+1}_{n+1}(1)$ or $H^{2n+1}_{n}(-1)$. We also show that f is an equiaffine sphere, i.e. the centroaffine normal is a constant multiple of the Blaschke normal, if and only if g is minimal.
LA - eng
KW - affine differential geometry; affine hyperspheres; product structures
UR - http://eudml.org/doc/282229
ER -