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arXiv · 2005.06395

Totally umbilical submanifolds in pseudo-Riemannian space forms

Yuichiro Sato
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Abstract

A totally umbilical submanifold in pseudo-Riemannian manifolds is a fundamental notion, which is characterized by the condition that the second fundamental form is proportional to the metric. It is also a generalization of the notion of a totally geodesic submanifold. In this paper, we classify congruent classes of full totally umbilical submanifolds in non-flat pseudo-Riemannian space forms, and consider their moduli spaces. As a consequence, we show that some moduli spaces of isometric immersions between space forms which one of the same constant curvature are non-Hausdorff.

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Yuichiro Sato. 2020-05-13. Totally umbilical submanifolds in pseudo-Riemannian space forms. https://arxiv.org/abs/2005.06395

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