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Flat Hyperbolic Centro-affine Tchebychev Hypersurfaces of $$\mathbb {R}^{4}$$ by Sébastien Lalléchère; Lucius Ramifidisoa; Blaise Ravelo is a Mathematics article available to read on EtoBox.

What is Flat Hyperbolic Centro-affine Tchebychev Hypersurfaces of $$\mathbb {R}^{4}$$ about?

We study centro-affine Tchebychev hyperbolic hypersurfaces M in R 4 , which satisfy the following conditions: for all X, Y, Z ∈ TpM : 1. M is flat, it means that the curvature tensor R associated with the Levi-Civita connection of the centro-affine metric satisfies R(X, Y )Z = 0; 2. The Tchebychev vector field T # satisfies ∇X T # = αX where α is a differentiable function on M , that is to say that M is a Tchebychev surface as introduced by Samelson from his work (Arch Ration Mech Anal 114:237-254) in 1991. So, we find Theorem 1 on the next page.

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Author

Sébastien Lalléchère; Lucius Ramifidisoa; Blaise Ravelo

Publisher

Springer Science and Business Media LLC

Published

2021

Language

EN

Field

Mathematics (Physical Sciences)