On Jacobi fields in quaternion Kaehler manifolds with constant $Q$-sectional curvature

Jacobi-Type Vector Fields on Kaehler Manifold

In this paper, we use the notion of Jacobi-type vector fields introduced in [5] to obtain a necessary and sufficient condition for a Kaehler manifold to be isometric to the complex space form (Cn, J, 〈, 〉), where J is the complex structure and 〈, 〉 is the Euclidean metric on Cn. Mathematics Subject Classification: 53C20, 53B21

Jacobi Fields on Statistical Manifolds of Negative Curvature

Abstract. Two entropic dynamical models are considered. The geometric structure of the statistical manifolds underlying these models is studied. It is found that in both cases, the resulting metric manifolds are negatively curved. Moreover, the geodesics on each manifold are described by hyperbolic trajectories. A detailed analysis based on the Jacobi equation for geodesic spread is used to sho...

Strictly Kähler-Berwald manifolds with constant‎ ‎holomorphic sectional curvature

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

integral inequalities for submanifolds of hessian manifolds with constant hessian sectional curvature

in this paper, we obtain two intrinsic integral inequalities of hessian manifolds.

Lecture on Kaehler manifolds