A Global Approach to the Theory of Special Finsler Manifolds
نویسندگان
چکیده
The aim of the present paper is to provide a global presentation, as complete as we can, of the theory of special Finsler manifolds. We introduce and investigate globally (or intrinsically, free from local coordinates) many of the most important and commonly used special Finsler manifolds : locally Minkowskian, Berwald, Landesberg, general Landesberg, P -reducible, C-reducible, semi-C-reducible, quasi-C-reducible, P -Finsler, C-recurrent, C-recurrent, C-recurrent, S-recurrent, S-recurrent of the second order, C2-like, S3-like, S4-like, P2-like, R3-like, P -symmetric, h-isotropic, of scalar curvature, of constant curvature, of p-scalar curvature, of s-pscurvature. The global definitions of such special Finsler manifolds are introduced. Various relationships between the different types of special Finsler manifolds are found. Many local results, existing in the literature, are proved globally and other new results are obtained. As a by-product, interesting identities and properties concerning the torsion tensor fields and the curvature tensor fields are deduced. Although our investigation is entirely global, we provide; for the sake of completeness and for comparison reasons, an appendix presenting a local survey of our global approach and the local definitions of the special Finsler spaces treated.
منابع مشابه
On the k-nullity foliations in Finsler geometry
Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...
متن کاملLow dimensional flat manifolds with some classes of Finsler metric
Flat Riemannian manifolds are (up to isometry) quotient spaces of the Euclidean space R^n over a Bieberbach group and there are an exact classification of of them in 2 and 3 dimensions. In this paper, two classes of flat Finslerian manifolds are stuided and classified in dimensions 2 and 3.
متن کاملOn Stretch curvature of Finsler manifolds
In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied. In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...
متن کاملRelative 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 کامل