Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 54, Number 3 (2002), 551-564.
Higher rank curved Lie triples
A substantial proper submanifold of a Riemannian symmetric space is called a curved Lie triple if its tangent space at every point is invariant under the curvature tensor of , 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: must be intrinsically locally symmetric. In fact we conjecture that is an extrinsically symmetric isotropy orbit. We are able to prove this conjecture provided that a tangent space of is also a tangent space of such an orbit.
J. Math. Soc. Japan, Volume 54, Number 3 (2002), 551-564.
First available in Project Euclid: 5 October 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
ESCHENBURG, Jost-Hinrich. Higher rank curved Lie triples. J. Math. Soc. Japan 54 (2002), no. 3, 551--564. doi:10.2969/jmsj/1191593908. https://projecteuclid.org/euclid.jmsj/1191593908