Homogeneous Riemannian manifolds covered by $S^{m}\times S^{n}$

The Manifolds Covered by a Riemannian Homogeneous Manifold

Flat Homogeneous Pseudo-Riemannian Manifolds

The complete homogeneous pseudo-Riemannian manifolds of constant non-zero curvature were classified up to isometry in 1961 [1]. In the same year, a structure theory [2] was developed for complete fiat homogeneous pseudo-Riemannian manifolds. Here that structure theory is sharpened to a classification. This completes the classification of complete homogeneous pseudo-Riemannian manifolds of arbit...

Complete k-Curvature Homogeneous Pseudo-Riemannian Manifolds

For k 2, we exhibit complete k-curvature homogeneous neutral signature pseudoRiemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous). All the local scalar Weyl invariants of these manifolds vanish. These manifolds are Ricci flat, Osserman, and Ivanov–Petrova. Mathematics Subject Classification (2000): 53B20.

Maximal Complexifications of Certain Homogeneous Riemannian Manifolds

Let M = G/K be a homogeneous Riemannian manifold with dimCGC = dimRG, where GC denotes the universal complexification of G. Under certain extensibility assumptions on the geodesic flow of M , we give a characterization of the maximal domain of definition in TM for the adapted complex structure and show that it is unique. For instance, this can be done for generalized Heisenberg groups and natur...

Maximal Complexifications of Certain Riemannian Homogeneous Manifolds

Let M = G/K be a Riemannian homogeneous manifold with dimCG C = dimRG , where G C denotes the universal complexification of G. Under certain extensibility assumptions on the geodesic flow of M , we give a characterization of the maximal domain of definition in TM for the adapted complex structure and show that it is unique. For instance, this can be done for generalized Heisenberg groups and na...