Nearly Kahler homogeneous manifolds with positive curvature

2009/04/03 by Davila, J. C. Gonzalez, Cabrera, F. Martin
#53C20 #53C30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0904.0572

Abstract

We prove that a 2n-dimensional compact homogeneous nearly Kahler manifold with strictly positive sectional curvature is isometric to CPⁿ, equipped with the symmetric Fubini-Study metric or with the standard Sp(m)-homogeneous metric, n =2m-1, or to S⁶ as Riemannian manifold with constant sectional curvature. This is a positive answer for a revised version of a conjecture given by Gray.

Related

• Homogeneous nearly Kähler manifolds
• Homogeneous nearly Kähler manifolds
• Quasi-positive curvature on homogeneous bundles
• Quaternionic-Kähler manifolds with nonnegative sectional curvature
• Isometry groups of nearly Kähler manifolds