The Cr-geometry of the Complex Indicatrix
نویسنده
چکیده
In this paper is studied the differential geometry of the complex indicatrix, which is approached as an embedded CR hypersurface of the punctual holomorphic tangent bundle of a complex Finsler space. Following the study of CR submanifolds of a Kähler manifold and using the submanifold formulae there are investigated some properties of the complex indicatrix, such as the fact that it is an extrinsic hypersphere of the holomorphic tangent space. The fundamental equations of the indicatrix as a real submanifold of codimension 1 are also determined. Besides this, the CR-structure integrability is studied and the Levi form and characteristic direction of the complex indicatrix are given. AMS Mathematics Subject Classification (2010): 53B40, 53C60, 53C40, 53B25.
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