Finsler connection preserving the two-vector angle under the indicatrix-inhomogeneous treatment

2011/09/13 by G. S. Asanov, Asanov, G. S.
Physics and Astronomy · #53A35 #53B40 #53B50 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1109.2673

openalex publication_date 2011/09/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The Finsler spaces in which the tangent Riemannian spaces are conformally flat prove to be characterized by the condition that the indicatrix is a space of constant curvature. In such spaces the Finslerian normalized two-vector angle can be explicated from the respective two-vector angle of the associated Riemannian space. Therefore the way is opening to propose explicitly the connection preserving the angle even at the indicatrix-inhomogeneous level, that is, when the indicatrix curvature value \mathcal C_Ind. is permitted to be an arbitrary smooth function of the indicatrix position point x. The connection obtained is metrical with the deflection part which is proportional to the gradient of the function H(x) entering the equality \mathcal C_Ind. ≡ H². Also the connection is covariant-constant. When the transitivity of covariant derivative is used, from the commutators of covariant derivatives the associated curvature tensor is found. Various useful representations have been developed. The Finsleroid space has been explicitly outlined.

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