Bi-Hermitian gray surfaces II

TL;DR

This paper classifies bi-Hermitian compact surfaces with a specific Ricci tensor condition, advancing understanding of their geometric structure.

Contribution

It provides a classification of bi-Hermitian compact surfaces satisfying a particular Ricci tensor relation, extending previous work in complex differential geometry.

Findings

Identification of all bi-Hermitian surfaces meeting the Ricci condition

Characterization of geometric structures satisfying the tensor relation

Extension of classification results in complex surface theory

Abstract

The aim of this paper is to classify bi-Hermitian compact surfaces $(M,g)$ whose Ricci tensor $\rho$ satisfies the relation $\nabla_X\rho(X,X) =\frac13X\tau g(X,X)$.