We obtain on a Kähler B-manifold (i.e., manifold with Norden metric) some corresponding results from the Kählerian and para-Kählerian context concerning Bochner curvature. prove that such is of constant totally real sectional curvatures if only it holomorphic Einstein, flat manifold. Moreover, we provide necessary sufficient conditions for gradient Ricci soliton or ?-Einstein metric to be flat....

a cartan manifold is a smooth manifold m whose slit cotangent bundle 0t *m is endowed with a regularhamiltonian k which is positively homogeneous of degree 2 in momenta. the hamiltonian k defines a (pseudo)-riemannian metric ij g in the vertical bundle over 0 t *m and using it, a sasaki type metric on 0 t *m is constructed. a natural almost complex structure is also defined by k on 0 t *m in su...

A Riemannian manifold (M, ρ) is called Einstein if the metric ρ satisfies the condition Ric(ρ) = c · ρ for some constant c. This paper is devoted to the investigation of G-invariant Einstein metrics with additional symmetries, on some homogeneous spaces G/H of classical groups. As a consequence, we obtain new invariant Einstein metrics on some Stiefel manifolds SO(n)/SO(l), and on the symplecti...

We introduce the notion of a special monopole class on a four-manifold. This is used to prove restrictions on the smooth structures of Einstein manifolds. As an application we prove that there are Einstein four-manifolds which are simply connected, spin, and satisfy the strict Hitchin–Thorpe inequality, and which are homeomorphic to manifolds without Einstein metrics.

It is proved that for a non-Sasakian η-Einstein (κ, μ)-manifold M the following three conditions are equivalent: (a) M is flat and 3-dimensional, (b) M is Ricci-semisymmetric, and (c) M is ξ-Riccisemisymmetric. Then it is proved that an ξ-Ricci-semisymmetric (κ, μ)manifold M is either flat and 3-dimensional, or locally isometric to E × S(4), or an Einstein-Sasakian manifold. Mathematics Subject...

We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.

We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.

We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.

We prove that a Sasakian 3-manifold admitting a non-trivial solution to the Einstein-Dirac equation has necessarily constant scalar curvature. In the case when this scalar curvature is non-zero, their classi cation follows then from a result by Th. Friedrich and E.C. Kim. We also prove that a scalarat Sasakian 3-manifold admits no local Einstein spinors.

The Ricci soliton condition reduces to a set of ODEs when one assumes that the metric is a doubly-warped product of a ray with a sphere and an Einstein manifold. If the Einstein manifold has positive Ricci curvature, we show there is a one-parameter family of solutions which give complete non-compact Ricci solitons.