Some harmonic problems on the tangent bundle with a Berger-type deformed Sasaki metric

TL;DR

This paper investigates harmonic maps related to the tangent bundle of an almost anti-paraHermitian manifold equipped with a Berger-type deformed Sasaki metric, focusing on the harmonicity of the projection and vector fields.

Contribution

It studies harmonicity conditions for the tangent bundle with a Berger-type deformed Sasaki metric, a novel geometric structure in this context.

Findings

Harmonicity conditions for the projection map are established.

Harmonicity criteria for vector fields as maps are derived.

Results extend understanding of harmonic maps in deformed tangent bundle geometries.

Abstract

Let $(M_{2k},\varphi ,g)$ be an almost anti-paraHermitian manifold and $(TM,g_{BS})$ be its tangent bundle with a Berger type deformed Sasaki metric $g_{BS}$. In this paper, we deal with the harmonicity of the canonical projection $\pi :TM\rightarrow M$ and a vector field $\xi $ which is considered as a map $\xi :M\rightarrow TM$.