Virtual immersions, and a characterization of symmetric spaces
Differential Geometry
2017-12-01 v1
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.
Keywords
Cite
@article{arxiv.1711.11435,
title = {Virtual immersions, and a characterization of symmetric spaces},
author = {Ricardo A. E. Mendes and Marco Radeschi},
journal= {arXiv preprint arXiv:1711.11435},
year = {2017}
}
Comments
11 pages. arXiv admin note: text overlap with arXiv:1708.05881