Geodesic
The CR-geometry of the complex indicatrix
Novi Sad Journal of Mathematics, Tome 46 (2016) no. 1.

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In this paper we study 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 K\"{a}hler manifold and using the submanifold formulae we investigate 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.
Publié le :
DOI : 10.30755/NSJOM.03220
Classification : 53B40, 53C60, 53C40, 53B25
Keywords: complex Finsler space, complex indicatrix, CR hypersurface, extrinsic sphere, fundamental equations, Levi form 
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Elena Popovici. The CR-geometry of the complex indicatrix. Novi Sad Journal of Mathematics, Tome 46 (2016) no. 1. doi : 10.30755/NSJOM.03220. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.03220/

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