Geometric realizations of curvature models by manifolds with constant scalar curvature

TL;DR

This paper demonstrates that various curvature models, including Riemannian and pseudo-Hermitian types, can be realized by manifolds with constant scalar or *-scalar curvature, providing a geometric realization framework.

Contribution

It introduces a method to realize diverse curvature models through manifolds with constant scalar or *-scalar curvature, extending geometric realization results.

Findings

Riemannian curvature models can be realized with constant scalar curvature.

Pseudo-Hermitian, para-Hermitian, hyper-pseudo-Hermitian, and hyper-para-Hermitian models can be realized with constant scalar and *-scalar curvature.

The paper establishes a unifying realization approach for multiple curvature models.

Abstract

We show any Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyper-pseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with constant scalar and *-scalar curvature.