Properties of complete non-compact Kähler surfaces of negative Ricci curvature.
Our main purpose of this paper is to introduce a natural generalization of the Bochner curvature tensor on a Hermitian manifold provided with the Hermitian connection. We will call the pseudo-Bochner curvature tensor. Firstly, we introduce a unique tensor P, called the (Hermitian) pseudo-curvature tensor, which has the same symmetries as the Riemannian curvature tensor on a Kähler manifold. By using P, we derive a necessary and sufficient condition for a Hermitian manifold to be of pointwise...
Soit un ouvert relativement compact et localement pseudo-convexe de la variété analytique .Alors,1) Si le fibré tangent est positif, est -convexe.2) Si admet une fonction strictement plurisousharmonique, est de Stein.3) Si est l’espace total d’un morphisme de Stein à base de Stein, est de Stein.
The aim of this paper is to describe all Kähler manifolds with quasi-constant holomorphic sectional curvature with κ = 0.
Lee, Kim and Suh (2012) gave a characterization for real hypersurfaces of Type in complex two plane Grassmannians with a commuting condition between the shape operator and the structure tensors and for in . Motivated by this geometrical notion, in this paper we consider a new commuting condition in relation to the shape operator and a new operator induced by two structure tensors and . That is, this commuting shape operator is given by . Using this condition, we prove that...
In this paper, first we introduce a new notion of commuting condition that between the shape operator and the structure tensors and for real hypersurfaces in . Suprisingly, real hypersurfaces of type , that is, a tube over a totally geodesic in complex two plane Grassmannians satisfy this commuting condition. Next we consider a complete classification of Hopf hypersurfaces in satisfying the commuting condition. Finally we get a characterization of Type in terms of such commuting...
We characterize real hypersurfaces with constant holomorphic sectional curvature of a non flat complex space form as the ones which have constant totally real sectional curvature.
We show that if a polarised manifold admits an extremal metric then it is K-polystable relative to a maximal torus of automorphisms.