On homogeneous Hermite-Lorentz spaces

TL;DR

This paper introduces Hermite-Lorentz metrics on almost-complex manifolds, explores their properties, and analyzes the structure of their isometry groups within the context of pseudo-Riemannian geometry.

Contribution

It defines Hermite-Lorentz metrics on almost-complex manifolds and investigates their isometry groups, providing new insights into their geometric structure.

Findings

Hermite-Lorentz metrics are compatible with almost complex structures.

The structure of isometry groups for these metrics is characterized.

New classes of pseudo-Riemannian metrics are identified on complex manifolds.

Abstract

We define naturally Hermite-Lorentz metrics on almost-complex manifolds as special case of pseudo-Riemannian metrics compatible with the almost complex structure. We study their isometry groups.