Geometric Realizability of Covariant Derivative K\"ahler Tensors for almost Pseudo-Hermitian and almost Para-Hermitian Manifolds

TL;DR

This paper characterizes the algebraic conditions of covariant derivative K"ahler tensors in almost pseudo-Hermitian and para-Hermitian manifolds and proves their geometric realizability.

Contribution

It establishes a correspondence between algebraic relations of covariant derivative K"ahler tensors and their geometric realization in specific manifolds.

Findings

Any 3-tensor satisfying the algebraic relations can be realized geometrically.

Provides a complete characterization of covariant derivative K"ahler tensors.

Bridges algebraic conditions with geometric structures in almost pseudo-Hermitian and para-Hermitian manifolds.

Abstract

The covariant derivative of the K\"ahler form of an almost pseudo-Hermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which satisfies these algebraic relations can be realized geometrically.