Bi-Hermitian and locally conformally K\"ahler surfaces

TL;DR

This paper explores the relationships between bi-Hermitian metrics and locally conformally K"ahler metrics on complex surfaces, shedding light on their interconnections and properties.

Contribution

It provides new insights into the interplay between bi-Hermitian and locally conformally K"ahler structures on complex surfaces.

Findings

Identifies key relations between the two metric types

Provides conditions under which these structures coexist

Enhances understanding of complex surface geometry

Abstract

We report on a few interrelations between bi-Hermitian metrics and locally conformally K\"ahler metrics on complex surfaces.