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.
Citation
Yuichiro Sato. "Totally umbilical submanifolds in pseudo-Riemannian space forms." Tsukuba J. Math. 45 (2) 97 - 116, December 2021. https://doi.org/10.21099/tkbjm/20214502097
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