Sasakian Finsler structures on pulled-back bundle

TL;DR

This paper introduces and studies almost contact and normal almost contact Finsler structures on pulled-back bundles, exploring their properties and characterizations related to Sasakian and K-contact structures using curvature tensors.

Contribution

It presents new concepts of Finsler structures on pulled-back bundles and provides characterizations of Finslerian K-contact structures using curvature tensors.

Findings

Properties of partly Sasakian structures are analyzed.

Characterizations of horizontally Finslerian K-contact structures are obtained.

Relations between curvature tensors and Finsler structures are established.

Abstract

Under a pulled-back approach given in [1] and firstly presented in [2], we introduce, in this paper, the concepts of almost contact and normal almost contact Finsler structures on the pulled-back bundle. Properties of structures partly Sasakians are studied. Using the hh-curvature tensor of Chern connection given in [2], we obtain some characterizations of horizontally Finslerian K-contact structures via the horizontal Ricci tensor and the flag curvature.