A new general Finsler connection

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt. E-mail: salahelgendi@yahoo.comy

2 Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt. E-mail: amrsoleiman@yahoo.com

3 Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt. E-mail: a.m.abdelsalam@fsc.bu.edu.eg

Abstract

The theory of connections is an important field of research in differential geometry. It was initially developed to solve pure geometrical problems. In the Riemannian contex, M. M. Tripathi introduced a new linear connection on a Riemannian manifold, which generalizes many Riemannian connections such as symmetric, semi-symmetric, qurter-symmetric; Ricci qurter-symmetric; metric, non-metric and recurrent connections. In this paper, we extend the work of M. M. Tripath from Riemannian geometry to Finsler geometry, precisely, we investigate a new linear Finsler connection, which unifies the well known linear connections and provides new connections in Finsler geometry. This connection will be named general linear Finsler (GF-) connection. The existence and uniqueness of such a connection is proved. The curvature and torsion tensors are computed. A general reformulation for Cartan, Berwald, Chern and Hashiguchi connections is obtained. Various special cases and connections are studied and introduced. Moreover, some examples of this connection are studied.

Keywords

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Journal of Finsler Geometry and its Applications
Volume 1, Issue 1
July 2020
Pages 1-14

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