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arXiv · 1711.11435

Virtual immersions, and a characterization of symmetric spaces

Ricardo A. E. Mendes·Marco Radeschi
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Abstract

We define virtual immersions, as a generalization of isometric immersions in a pseudo-Riemannian vector space. We show that virtual immersions possess a second fundamental form, which is in general not symmetric. We prove that a manifold admits a virtual immersion with skew symmetric second fundamental form, if and only if it is a symmetric space, and in this case the virtual immersion is essentially unique.

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Ricardo A. E. Mendes, Marco Radeschi. 2017-11-28. Virtual immersions, and a characterization of symmetric spaces. https://arxiv.org/abs/1711.11435

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