Transilvania University of Brasov
Abstract: Following the study of the indicatrix of a real Finsler space, in this paper there are investigated some properties of the complex indicatrix of a complex Finsler space, both in a fixed point and for the indicatrix bundle. Using the submanifold equations, several properties of the indicatrix in a fixed point are obtained in terms of the fundamental function. In the global case, an almost contact structure is introduced on the indicatrix bundle and considering the Gauss-Weingarten equations with respect to the Chern-Finsler connection, a constant value of the mean curvature is determined.
Keywords: Complex Finsler space, indicatrix, mean curvature, totally umbilical, Gauss equations, Weingarten formula, Ricci tensor.
Classification (MSC2000): 53B40; 53C60, 53C40, 53B25
Full text of the article: