On left-invariant Einstein metrics that are not geodesic orbit

Invariant Shen connections and geodesic orbit spaces

The geodesic graph of Riemannian spaces all geodesics of which are orbits of 1-parameter isometry groups is constructed by J. Szenthe in 1976 and it became a basic tool for studying such spaces, called g.o. spaces. This infinitesimal structure corresponds to the reductive complement m in the case of naturally reductive spaces. The systematic study of Riemannian g.o. spaces is started by O. Kowa...

Projective Invariant Metrics for Einstein Spaces

Invariant Einstein Metrics on Flag Manifolds with Four Isotropy Summands

A generalized flag manifold is a homogeneous space of the form G/K, where K is the centralizer of a torus in a compact connected semisimple Lie group G. We classify all flag manifolds with four isotropy summands by the use of t-roots. We present new G-invariant Einstein metrics by solving explicity the Einstein equation. We also examine the isometric problem for these Einstein metrics. 2000 Mat...

on einstein (α,β )-metrics

– in this paper we consider some (α ,β ) -metrics such as generalized kropina, matsumoto and f (α β )2α = + metrics, and obtain necessary and sufficient conditions for them to be einstein metrics when βis a constant killing form. then we prove with this assumption that the mentioned einstein metrics must beriemannian or ricci flat.

A remark on left invariant metrics on compact Lie groups

The investigation of manifolds with non-negative sectional curvature is one of the classical fields of study in global Riemannian geometry. While there are few known obstruction for a closed manifold to admit metrics of non-negative sectional curvature, there are relatively few known examples and general construction methods of such manifolds (see [Z] for a detailed survey). In this context, it...