Some remarks on a minkowski space $(r^n, f)$

Tran Quoc Binh

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arXiv · 1406.0348

Some remarks on a minkowski space $(r^n, f)$

Tran Quoc Binh

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Abstract

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 $\hat{g}$.

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BibTeX RIS

Tran Quoc Binh. 2014-06-02. Some remarks on a minkowski space $(r^n, f)$. https://arxiv.org/abs/1406.0348

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