Nearly Kahler homogeneous manifolds with positive curvature
Abstract
We prove that a 2n-dimensional compact homogeneous nearly Kahler manifold with strictly positive sectional curvature is isometric to CP^{n}, equipped with the symmetric Fubini-Study metric or with the standard Sp(m)-homogeneous metric, n =2m-1, or to S^{6} as Riemannian manifold with constant sectional curvature. This is a positive answer for a revised version of a conjecture given by Gray.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2009
- DOI:
- 10.48550/arXiv.0904.0572
- arXiv:
- arXiv:0904.0572
- Bibcode:
- 2009arXiv0904.0572G
- Keywords:
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- Mathematics - Differential Geometry;
- 53C20;
- 53C30
- E-Print:
- 10 pages