2007/10/20 by G. S. Asanov, Asanov, G. S.
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP
paper · pdf · doi:10.48550/arxiv.0710.3814
arxiv created 2007/10/20 · openalex publication_date 2007/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Finsleroid-Finsler space is constructed over an underlying Riemannian space by the help of a scalar g(x) and an input 1-form b of unit length. Explicit form of the entailed tensors, as well as the respective spray coefficients, is evaluated. The involutive case means the framework in which the characteristic scalar g(x) may vary in the direction assigned by b, such that dg=μb with a scalar μ(x). We show by required calculation that the involutive case realizes through the A-special relation the picture that instead of the Landsberg condition Aijk=0 we have the vanishing \alijk=0 with the normalized tensor \alijk=Aijk/||A||. Under the involutive condition, the derivative tensor Ai|j and the curvature tensor Rik have explicitly been found, assuming the input 1-form b be parallel. Key words: Finsler metrics, spray coefficients, curvature tensors.