# Centroaffine differential geometry and its relations to horizontal submanifolds

Banach Center Publications (2002)

- Volume: 57, Issue: 1, page 21-28
- ISSN: 0137-6934

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topLuc 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 -

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