Properties of Critical Points of the Dinew-Popovici Energy Functional

Author:

Soheil Erfan1

Affiliation:

1. Institut de Mathématiques de Toulouse , Université Paul Sabatier , 118 route de Narbonne, 31062 Toulouse , France

Abstract

Abstract Recently, Dinew and Popovici introduced and studied an energy functional F acting on the metrics in the Aeppli cohomology class of a Hermitian-symplectic metric and showed that in dimension 3 its critical points (if any) are Kähler. In this article we further investigate the critical points of this functional in higher dimensions and under holomorphic deformations. We first prove that being a critical point for F is a closed property under holomorphic deformations. We then show that the existence of a Kähler metric ω in the Aeppli cohomology class is an open property under holomorphic deformations. Furthermore, we consider the case when the (2, 0)-torsion form ρω 2, 0 of ω is -exact and prove that this property is closed under holomorphic deformations. Finally, we give an explicit formula for the differential of F when the (2, 0)-torsion form ρω 2, 0 is -exact.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

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