Conformal β- change in Finsler spaces

2006/02/18 by S. H. Abed, Abed, S. H.
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc #math.DG

paper · pdf · doi:10.48550/arxiv.math/0602404

9 pages, tex file

openalex publication_date 2006/02/18 · arxiv created 2006/02/22 · arxiv updated 2009/12/01 · openalex created_date 2020/08/07 · openalex updated_date 2026/07/28

Abstract

We investigate what we call a conformal β - change in Finsler spaces, namely L(x,y)→ ~^∗L(x,y)=e^σ(x)L(x,y)+β(x,y) where~σ~ is a function of x~ only ~and ~ β(x, y) is a given 1- form. This change generalizes various types of changes: conformal changes, Randers changes and β - changes. Under this change, we obtain the relationships between some tensors associated with (M,L) and the corresponding tensors associated with (M,^∗L). We investigate some σ- invariant tensors . This investigation allows us to give an answer to the question: Are the properties of C-reducibility, S₃-likeness and S₄-likeness invariant under a conformal β - change?

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