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Some Remarks on a Minkowski Space $(R^n, F)$ by Binh, Tran Quoc is a scholarly article available to read on EtoBox.

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We consider a complete, totally umbilical hypersurface $M$ of Riemannian space $(\hat{R}^n, \hat{g})$ induced by a Minkowski space $(R^n, F)$. Under certain conditions we prove that $M$ is isometric to a "round" hypersphere of the $(n + 1)-$dimensional Euclidean space. We also prove that the Minkowski norm $F$ must be arised from an inner product if there exist a non-zero vector field, which is parallel according to Levi-Civita connection of the metric tensor $\hat{g}$.

Author

Binh, Tran Quoc

Published

2014

Language

EN