Geometric realizations of Kaehler and of para-Kaehler curvature models

TL;DR

This paper demonstrates that all Kaehler and para-Kaehler algebraic curvature tensors can be realized by corresponding manifolds with constant scalar curvature, bridging algebraic models and geometric structures.

Contribution

It establishes the geometric realizability of all Kaehler and para-Kaehler algebraic curvature tensors with constant scalar curvature.

Findings

Kaehler algebraic curvature tensors are realizable by Kaehler manifolds of constant scalar curvature

Para-Kaehler algebraic curvature tensors are realizable by para-Kaehler manifolds of constant scalar curvature

Provides a link between algebraic curvature models and geometric structures

Abstract

We show that every Kaehler algebraic curvature tensor is geometrically realizable by a Kaehler manifold of constant scalar curvature. We also show that every para-Kaehler algebraic curvature tensor is geometrically realizable by a para-Kaehler manifold of constant scalar curvature