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Concircular π-Vector Fields and Special Finsler Spaces
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt; Center for Theoretical Physics (CTP), The British University in Egypt (BUE), Cairo, Egypt
Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
- 1 Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt; Center for Theoretical Physics (CTP), The British University in Egypt (BUE), Cairo, Egypt
- 2 Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
Advances in Pure Mathematics·Volume 03 (2013)·Pages 282–291·Published 5 March 2013·DOI10.4236/apm.2013.32040
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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.
KeywordsFinsler ManifoldCartan ConnectionConcurrent π-Vector FieldConcircular π-Vector FieldSpecial Finsler SpaceRecurrent Finsler Space
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