On Concircular Transformations in Finsler Spaces

Authors
Urmia University
Abstract
Randers metrics are the most important class of Finsler metrics which is defined by a Riemannian metric and a 1-form as . In this paper, the concept of geodesic circle preserve transformations in Finslerian space is studied and the weak Einstein Randers metrics have been investigated. Further we prove this condition for Randers metric of weak isotropic flag curvature and weak isotropic Berwald curvature.



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Keywords

[1] Yano, K.: On circular geometry,I. Concircular transformations. Proc. Imp. Acad . Tokyo 16, 195-200 (1940).

[2] Yano, K.: On circular geometry, II. Integrability conditions of ρ_μλ=ϕg_μλ. Proc. Imp. Acad. Tokyo 16, 505-511 (1940).

[3] Yano, K.: On circular geometry, III. Theory of curves. Proc. Imp. Acad. Tokyo 16, 442-448 (1940).

[4] Yano, K.: On circular geometry, IV. Theory of subspace. Proc. Imp. Acad. Tokyo 18, 505-511 (1940).

[5] Yano, K.: On circular geometry, V. Einstein spaces. Proc. Imp. Acad. Tokyo 18, 446-451 (1942).

[6] Vogel, W.O.K.: Transformationen in Riemannschen Ra ̈umen, (German). Arch. Math. Soc. 117, 251-275 (1965).

[7] Ishihara, S.: On infinitesimal concircular transformations. K ̂odai Math. Sem. Rep. 12, 45-56 (1960).

[8] Ferrand, J.: Concircular transformations of Riemannian manifolds. Ann. Acad. Sci. Fenn. M. 10, 163-171 (1985).

[9] Bidabad B., Shen Z.,: Circle-preserving transformations in Finsler spaces. Publ. Math. Debr. 81, 435-445 (2012).

[10] Bidabad, B.: A classification of complete Finsler manifolds through the conformal theory of curves. Differential geometry and its applications 35, 350-360 (2014).

[11] Shen Z., Yang G.: On concircular transformations in Finsler geometry. Results Math. 74:162 (2019).

[12] Bao D., Chern S.S., Shen Z. Riemannn-Finsler geometry, Springer-Verlag, (2000).