On the symmetries of a Kaehler manifold

TL;DR

This paper investigates the symmetries of Kähler manifolds, focusing on constant holomorphic sectional curvature, semisymmetric, and holomorphically pseudosymmetric cases, providing characterizations and geometric insights into the complex Tachibana tensor.

Contribution

It offers new characterization results and geometric interpretations for various symmetry types of Kähler manifolds, including the complex Tachibana tensor.

Findings

Characterization of constant holomorphic sectional curvature Kähler manifolds

Geometric interpretation of the complex Tachibana tensor

Results on semisymmetric and holomorphically pseudosymmetric Kähler manifolds

Abstract

In this manuscript we study natural symmetries of Kaehler manifolds: constant holomorphic sectional curvature Kaheler manifolds, semisymmetric Kaehler manifolds and holomorphically pseudosymmetric Kaehler manifolds. We get characterization results, as well as a geometric interpretation of the complex Tachibana tensor.