H-projectively Equivalent Kahler Manifolds and Gravitational Instantons

TL;DR

This paper investigates four-dimensional Kahler manifolds with H-projective mappings, focusing on Einstein-Kahler manifolds that can be viewed as gravitational instantons, exploring their geometric properties and classifications.

Contribution

It provides a detailed analysis of H-projectively equivalent Einstein-Kahler manifolds and their role as gravitational instantons, offering new insights into their geometric structure.

Findings

Classification of H-projectively equivalent Einstein-Kahler manifolds

Identification of conditions for gravitational instanton interpretation

New geometric properties of these manifolds

Abstract

The goal of the present paper is to investigate four dimensional Kahler manifolds admitting H-projective mappings with special attention to Einstein-Kahler manifolds of this type which can be interpreted as field configurations of the gravitational instantons.