Abstract
In the present paper, a complex Randers space with the metric \( F = \alpha + \varepsilon \left| \beta \right| + k\frac{{\left| \beta \right|^{2} }}{\alpha },\varepsilon ,k \ne 0 \) is introduced and expressions for fundamental metric tensor, angular metric tensor, Chern–Finsler connection coefficients and curvature are obtained.
This is a preview of subscription content, log in via an institution to check access.
References
Finsler P (1951) Uber Kurven and flacken in Allgemeinen Raumen (dissertation Gottingen 1918). Springer, Berlin
Rizza G (1963) Strutture di Finsler di Tipo quasi hermitiano. Riv Mat Univ Parma 4:83–106
Kobayashi S (1967) Distance, holomorphic mappings and the Schwarz lemma. J Math Soc Jpn 19(4):481–485
Abate M, Patrizio G (1994) Finsler metrics: a global approach with applications to geometric function theory. Springer, Berlin
Shen Z, Yildirim GC (2008) On a class of projectively Flat metric with constant Flag curvature. Can J Math 60:443–456
Aldea N, Munteanu G (2009) On complex Finsler spaces with Randers metric. J Korean Math Soc 46(5):949–966
Bao D, Chern SS, Shen Z (2000) An introduction to Riemann–Finsler geometry. Graduate Texts in Mathematics 200. Springer, New York
Bao D, Robles C, Shen Z (2004) Zermelo navigation on Riemannian manifolds. J Differ Geom 66(3):377–435
Yasuda H, Shimada H (1977) On Randers spaces of scalar curvature. Rep Math Phys 11(3):347–360
Matsumoto M (1989) Randers spaces of constant curvature. Rep Math Phys 28(2):249–261
Abate M, Patrizio A (1994) Finsler metric—a global approach with applications to geometric function theory, Lecture Notes in Mathematics, vol 1591. Springer, Berlin
Aikou T (2003) Projective flatness of complex Finsler metrics. Publ Math Debrecen 63(3):343–362
Munteanu G (2004) Complex spaces in Finsler, Lagrange and Hamilton geometries. Fundamental Theories of Physics. Kluwer Academic Publishers, Dordrecht
Spir A (2001) The structure equations of a complex Finsler manifold. Asian J Math 5(2):291–326
Aldea N, Munteanu G (2006) (α, β)-complex Finsler metrices. In: Proceedings of the 4th International Colloquium “Mathematics in Engineering and National Physics”, Burcharet, Romania, pp 1–6
Aldea N, Munteanu G (2006) On the geometry of Complex Randers space. In: Proceedings of the 14th Nat. Sem. On Finsler, Lagrange and Hamilton spaces, Brasov, pp 1–8
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kumari, S., Pandey, P.N. On a Complex Randers Space. Natl. Acad. Sci. Lett. 42, 123–130 (2019). https://doi.org/10.1007/s40009-018-0700-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40009-018-0700-8