Beil metrics in complex Finsler geometry
نویسنده
چکیده
In this paper we continue the study of the complex Beil metrics, in complex Finsler geometry, [18]. Primarily, we determine the main geometric objects corresponding to these metrics, e.g. the Chern-Finsler complex non-linear connection, the Chern-Finsler complex linear connection and the holomorphic curvature. We focus our study on the cases when a complex Finsler space, endowed with a complex Beil metric, becomes weakly Kähler and Kähler. Also, our study proves that a given complex Finsler metric is projectively related to its associated complex Beil metric. As an application of this theory, we set the variational problem of the complex Beil metric constructed with the weakly gravitational metric. In this case we find the Chern-Finsler complex non-linear connection by using another approach. M.S.C. 2010: 53B40, 53C60.
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