Almost Paracontact Finsler Structures on Vector Bundle

TL;DR

This paper introduces and analyzes almost paracontact Finsler structures on vector bundles, exploring their properties, integrability conditions, and curvature characteristics, including flag and Ricci curvatures, with implications for geometric structure classification.

Contribution

It defines new classes of paracontact Finsler structures on vector bundles and investigates their curvature properties and integrability conditions, advancing the understanding of their geometric behavior.

Findings

Vertical and horizontal flag curvatures are computed for K-paracontact Finsler structures.

Locally symmetric para-Sasakian Finsler structures have negative vertical ?-flag curvature.

Curvature properties of Ricci tensors in para-Sasakian Finsler structures are studied.

Abstract

In this paper, we define almost paracontact and normal almost paracontact Finsler structures on a vector bundle and find some conditions for integrability of these structures. We define paracontact metric, para- Sasakian and K-paracontact Finsler structures and study some properties of these structures. For a K-paracontact Finsler structure, we find the vertical and horizontal flag curvatures. Then, we define vertical ?-flag curvature and prove that every locally symmetric para-Sasakian Finsler structure has negative vertical ?-flag curvature. Finally, we define the horizontal and vertical Ricci tensors of a para-Sasakian Finsler structure and study some curvature properties of them.