From locally conformally K\"ahler to bi-Hermitian structures on non-K\"ahler complex surfaces

TL;DR

This paper demonstrates how locally conformally K"ahler metrics on specific non-K"ahler complex surfaces can be deformed into bi-Hermitian metrics, expanding the understanding of complex surface structures.

Contribution

It introduces a deformation method transforming locally conformally K"ahler metrics into bi-Hermitian metrics on certain compact complex surfaces.

Findings

Locally conformally K"ahler metrics can be deformed into bi-Hermitian metrics.

Applicable to complex surfaces with odd first Betti number.

Provides new examples of bi-Hermitian structures.

Abstract

We prove that locally conformally K\"ahler metrics on certain compact complex surfaces with odd first Betti number can be deformed to new examples of bi-Hermitian metrics.