Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 31, No. 1, pp. 107-120 (2015)

Some properties of the indicatrix of a complex Finsler space

Elena Popovici

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

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