# On the geometry of trans-para-Sasakian manifolds

## TL;DR

This paper introduces trans-para-Sasakian manifolds, exploring their geometric properties and curvature, and establishing conditions for them to be η-Einstein or Einstein, expanding the understanding of these structures.

## Contribution

It defines trans-para-Sasakian manifolds and investigates their curvature properties, providing new conditions for Einstein and η-Einstein classifications.

## Key findings

- Identification of curvature properties of trans-para-Sasakian manifolds
- Conditions for manifolds to be η-Einstein or Einstein
- Extension of trans-Sasakian geometry to the para setting

## Abstract

In this paper, we introduce the trans-para-Sasakian manifolds and we study their geometry. These manifolds are an analogue of the trans-Sasakian manifolds in the Riemannian geometry. We shall investigate many curvature properties of these manifolds and we shall give many conditions under which the manifolds are either $\eta-$Einstein or Einstein manifolds.