We prove that every Kähler metric, whose potential is a function of the timelike distance in the flat Kähler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local classification of the Kähler manifolds with the above mentioned metrics. New examples of Sasakian space forms are obtained as real hypersurfaces of a Kähler space form ...

Recently Demailly and Kóllar have developed some new techniques to study the existence of Kähler-Einstein metrics on compact Fano orbifolds [DK]. Johnson and Kóllar applied these techniques to study Kähler-Einstein metrics on certain log del Pezzo surfaces in weighted projective 3-spaces [JK1] as well as anti-canonically embedded orbifold Fano 3-folds in weighted projective 4-spaces [JK2]. In [...

We propose fundamental inequalities for contact pseudo-slant submanifolds of (ϵ)-para Sasakian space form employing generalized normalized δ-Casorati curvature. characterize which equality cases hold and illustrate the main result with some applications. Further, we have considered a certain type submanifold Ricci soliton after computing its scalar curvature, developed an inequality to find cor...