Universität zu Köln

Mendes, Ricardo A. E. and Radeschi, Marco ORCID: 0000-0001-6167-7136 (2019). Virtual immersions and a characterization of symmetric spaces. Ann. Glob. Anal. Geom., 55 (1). S. 43 - 54. DORDRECHT: SPRINGER. ISSN 1572-9060

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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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Mendes, Ricardo A. E. UNSPECIFIED UNSPECIFIED UNSPECIFIED Radeschi, Marco UNSPECIFIED orcid.org/0000-0001-6167-7136 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-157482
DOI:	10.1007/s10455-018-9617-1
Journal or Publication Title:	Ann. Glob. Anal. Geom.
Volume:	55
Number:	1
Page Range:	S. 43 - 54
Date:	2019
Publisher:	SPRINGER
Place of Publication:	DORDRECHT
ISSN:	1572-9060
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/15748