H-projectively-equivalent four-dimensional Kahler manifolds

TL;DR

This paper classifies four-dimensional Kahler manifolds with non-affine H-projective mappings, identifying non-Einstein cases, infinitesimal transformations, and providing explicit Ricci-flat metric formulas for generalized equidistant manifolds.

Contribution

It offers a complete classification of four-dimensional Kahler manifolds with H-projective mappings, including explicit metrics for Ricci-flat cases, advancing understanding of their geometric structures.

Findings

All non-Einstein four-dimensional Kahler manifolds with H-projective mappings are identified.

Infinitesimal H-projective transformations for these manifolds are characterized.

Explicit metrics for Ricci-flat generalized equidistant Kahler manifolds are derived.

Abstract

The paper is devoted to the investigation of four-dimensional Kahler manifolds admitting non-affine H-projective mappings. We find all such manifolds which are non-Einstein. In the paper also Kahler manifolds admitting infinitesimal H-projective transformations are determined. It is proved that the class of Kahler manifolds admitting H-projective mappings includes generalized equidistant Kahler manifolds. The explicit expression for the metrics of Ricci-flat four-dimensional generalized equidistant manifolds is given.