Indicatrix Geometry Clarifies that Finsler Length can be Larger than Relative Length
نویسندگان
چکیده
منابع مشابه
Relative volume comparison theorems in Finsler geometry and their applications
We establish some relative volume comparison theorems for extremal volume forms of Finsler manifolds under suitable curvature bounds. As their applications, we obtain some results on curvature and topology of Finsler manifolds. Our results remove the usual assumption on S-curvature that is needed in the literature.
متن کاملStructure of the indicatrix bundle of Finsler-Rizza manifolds
In this paper, we construct a framed f -structure on the slit tangent space of a Rizza manifold. This induces on the indicatrix bundle an almost contact metric. We find the conditions under which this structure reduces to a contact or to a Sasakian structure. Finally we study these structures on Kählerian Finsler manifolds. M.S.C. 2010: 53B40, 53C60, 32Q60, 53C15.
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In this note the geometry of the indicatrix (I, L̃) is studied as a hypersurface of a complex Finsler space (M,L). The induced Chern-Finsler and Berwald connections are defined and studied. The induced Berwald connection coincides with the intrinsic Berwald connection of the indicatrix bundle. We considered a special projection of a geodesic curve on a complex Finsler space (M,L), called the ind...
متن کاملThe Equations of the Indicatrix of a Complex Finsler Space
In this paper we extend the study of the indicatrix of a complex Finsler space initiated in [10, 11]. The equations that can be introduced on the indicatrix, which is studied as a hypersurface of a complex Finsler space, are investigated. In this manner, using the equations of Gauss-Weingarten, the link between the intrinsic and induced connection is deduced. The equations of Gauss, H -and A-Co...
متن کاملContact structures on the indicatrix of a complex Finsler space
Continuing the study of the complex indicatrix IzM , approached as an embedded CR hypersurface on the punctual holomorphic tangent bundle of a complex Finsler space, we study in this paper the almost contact structures that can be introduced on IzM . The Levi form and characteristic direction of the complex indicatrix are given and the CR distributions integrability is studied. Using these we c...
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ژورنال
عنوان ژورنال: Reports on Mathematical Physics
سال: 2018
ISSN: 0034-4877
DOI: 10.1016/s0034-4877(18)30068-5