Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On the symmetries of a Kaehler manifold

Alma L. Albujer, Jorge Alcázar, Magdalena Caballero

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.

On the symmetries of a Kaehler manifold

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.
Paper Structure (5 sections, 10 theorems, 46 equations, 1 table)

This paper contains 5 sections, 10 theorems, 46 equations, 1 table.

Table of Contents

  1. Introduction
  2. Set up
  3. The complex Tachibana tensor and constant holomorphic sectional curvature Kaehler manifolds
  4. Locally symmetric and semisymmetric Kaehler manifolds
  5. Holomorphically pseudosymmetric Kaehler manifolds

Key Result

Lemma 1

A Kaehler manifold $(M,g,J)$ has constant holomorphic sectional curvature if and only if $R(X,JX,X,Y)=0$ for every orthonormal subset $\{X,JX,Y\}$ in $\mathfrak{X}(M)$.

Theorems & Definitions (13)

  • Lemma 1
  • Lemma 2
  • Proposition 3
  • Proposition 4
  • Definition 1
  • Remark 1
  • Theorem 5
  • Theorem 6
  • Theorem 7
  • Definition 2
  • ...and 3 more