Harmonicity of the complex structure on product of trans-Sasakian manifolds

TL;DR

This paper studies the harmonicity of complex structures on product manifolds formed from trans-Sasakian manifolds, providing conditions and insights relevant to their geometric properties.

Contribution

It offers new conditions for the harmonicity of complex structures on product manifolds of trans-Sasakian manifolds and explores their relation to astheno-Kahler geometry.

Findings

Conditions for harmonic complex structures identified

Insights into harmonicity in astheno-Kahler manifolds

Analysis of Levi-Civita connection on product manifolds

Abstract

In this paper, we investigate the transverse geometry of trans-Sasakian manifolds and present several significant findings. We analyze the Levi-Civita connection associated with the metric on the product manifold of two trans-Sasakian manifolds. We outline the conditions under which the complex structure is harmonic on the product manifold. Notably, we also offer valuable insights into the harmonicity of the complex structure within the context of astheno- Kahler manifolds.