What question did this study set out to answer?

The study aims to characterize the geometry of Lorentzian trans-Sasakian manifolds with generalized Z-tensors.

April 24, 2026

Geometric Characterizations of Generalized Z-solitons on Lorentzian Trans-Sasakian 3-manifolds

Key Points

The study aims to characterize the geometry of Lorentzian trans-Sasakian manifolds with generalized Z-tensors.
Analyze the generalized Z-tensor under symmetry conditions like Codazzi type and cyclic parallel.
Derive constraints on the manifold structure based on tensor behavior.
Study the existence of generalized Z-Ricci solitons and their implications for scalar curvature.
Generalized Z-tensors exhibit specific behaviors under symmetry conditions.
The existence of generalized Z-Ricci solitons implies constant scalar curvature.
Such solitons typically display shrinking behavior.

Abstract

In this paper, we investigate the geometric characterizations of 3-dimensional Lorentzian trans-Sasakian manifolds admitting a generalized Z-tensor. First, we analyze the behavior of the generalized Z-tensor under certain symmetry conditions, such as Codazzi type, cyclic parallel, and -Z symmetric conditions, and derive the necessary constraints on the manifold structure. We also study the existence of generalized Z-Ricci solitons and prove that the existence of such a soliton implies that the scalar curvature is constant and the soliton generally exhibits a shrinking behavior.

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