Higher rank curved Lie triples

  • A substantial proper submanifold M of a Riemannian symmetric space S is called a curved Lie triple if its tangent space at every point is invariant under the curvature tensor of S, i.e. a sub-Lie triple. E.g. any complex submanifold of complex projective space has this property. However, if the tangent Lie triple is irreducible and of higher rank, we show a certain rigidity using the holonomy theorem of Berger and Simons: M must be intrinsically locally symmetric. In fact we conjecture that M is an extrinsically symmetric isotropy orbit. We are able to prove this conjecture provided that a tangent space of M is also a tangent space of such an orbit.

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Metadaten
Author:Jost-Hinrich EschenburgGND
URN:urn:nbn:de:bvb:384-opus4-392099
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/39209
ISSN:0025-5645OPAC
Parent Title (English):Journal of the Mathematical Society of Japan
Publisher:Mathematical Society of Japan (Project Euclid)
Place of publication:Tokyo
Type:Article
Language:English
Year of first Publication:2002
Publishing Institution:Universität Augsburg
Release Date:2018/07/30
Volume:54
Issue:3
First Page:551
Last Page:564
DOI:https://doi.org/10.2969/jmsj/1191593908
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Differentialgeometrie
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht