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July, 2002 Higher rank curved Lie triples
Jost-Hinrich ESCHENBURG
J. Math. Soc. Japan 54(3): 551-564 (July, 2002). DOI: 10.2969/jmsj/1191593908

Abstract

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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Jost-Hinrich ESCHENBURG. "Higher rank curved Lie triples." J. Math. Soc. Japan 54 (3) 551 - 564, July, 2002. https://doi.org/10.2969/jmsj/1191593908

Information

Published: July, 2002
First available in Project Euclid: 5 October 2007

zbMATH: 1066.53099
MathSciNet: MR1900956
Digital Object Identifier: 10.2969/jmsj/1191593908

Subjects:
Primary: 53C35
Secondary: 53B25, 53C24, 53C29

Rights: Copyright © 2002 Mathematical Society of Japan

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Vol.54 • No. 3 • July, 2002
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