On Kähler metrics in lorentzian manifolds
We study slant curves in contact Riemannian 3-manifolds with pseudo-Hermitian proper mean curvature vector field and pseudo-Hermitian harmonic mean curvature vector field for the Tanaka-Webster connection in the tangent and normal bundles, respectively. We also study slant curves of pseudo-Hermitian AW(k)-type.
In this paper we show that a 1-convex (i.e., strongly pseudoconvex) manifold , with 1- dimensional exceptional set and finitely generated second homology group , is embeddable in if and only if is Kähler, and this case occurs only when does not contain any effective curve which is a boundary.
In this paper, firstly we study some left invariant Riemannian metrics on para-hypercomplex 4-dimensional Lie groups. In each Lie group, the Levi-Civita connection and sectional curvature have been given explicitly. We also show these spaces have constant negative scalar curvatures. Then by using left invariant Riemannian metrics introduced in the first part, we construct some left invariant Randers metrics of Berwald type. The explicit formulas for computing flag curvature have been obtained in...
The object of the present paper is to study weakly -symmetric manifolds and its decomposability with the existence of such notions. Among others it is shown that in a decomposable weakly -symmetric manifold both the decompositions are weakly Ricci symmetric.