Special Einstein's equations on K\"ahler manifolds

TL;DR

This paper extends Stepanov's classification of Riemannian manifolds to Kähler manifolds by analyzing Einstein equations with a specific energy-momentum tensor form, reducing the number of classification classes.

Contribution

It introduces a specialized classification of Kähler manifolds based on Einstein equations with a particular energy-momentum tensor shape, refining previous Riemannian classifications.

Findings

Number of classes reduces in the Kähler case

Classification based on energy-momentum tensor properties

Extension of Stepanov's work to Kähler manifolds

Abstract

This work is devoted to the study of Einstein equations with a special shape of the energy-momentum tensor. Our results continue Stepanov's classification of Riemannian manifolds according to special properties of the energy-momentum tensor to K\"ahler manifolds. We show that in this case the number of classes reduces.