Concircular π-Vector Fields and Special Finsler Spaces

Nabil L. Youssef, Amr Soleiman

Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt.
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt; Center for Theoretical Physics (CTP), The British University in Egypt (BUE), Cairo, Egypt.

DOI: 10.4236/apm.2013.32040                

Abstract

The aim of the present paper is to investigate intrinsically the notion of a concircular π-vector field in Finsler geometry. This generalizes the concept of a concircular vector field in Riemannian geometry and the concept of concurrent vector field in Finsler geometry. Some properties of concircular π-vector fields are obtained. Different types of recurrence are discussed. The effect of the existence of a concircular π-vector field on some important special Finsler spaces is investigated. Almost all results obtained in this work are formulated in a coordinate-free form.

Keywords

Finsler Manifold; Cartan Connection; Concurrent π-Vector Field; Concircular π-Vector Field; Special Finsler Space, Recurrent Finsler Space

Conflicts of Interest

The authors declare no conflicts of interest.

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