Deformations of Vaisman manifolds

TL;DR

This paper introduces a new method for deforming Vaisman manifolds that preserves their canonical foliation, utilizing basic 1-forms with specific properties, which are shown to be plentiful.

Contribution

The authors develop a transverse deformation technique for Vaisman manifolds based on basic 1-forms, expanding the understanding of their geometric structures.

Findings

Existence of abundant basic 1-forms with required properties.

Construction of transverse deformations preserving the canonical foliation.

New insights into the geometric flexibility of Vaisman manifolds.

Abstract

We construct a type of transverse deformations of a Vaisman manifold, which preserves the canonical foliation. For this construction we only need a basic 1-form with certain properties. We show that such basic 1-forms exist in abundance.