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.
Author: | Jost-Hinrich EschenburgGND |
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URN: | urn:nbn:de:bvb:384-opus4-392099 |
Frontdoor URL | https://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 |