منابع مشابه
Unicorns in Finsler Geometry
By unicorns, I am referring to those mythical single-horned horse-like creatures for which there are only rumoured sightings by a privileged few. A similar situation exists in Finsler differential geometry. There, one has the hierarchy Euclidean ⊂ Minkowskian & Riemannian ⊂ Berwald ⊂ Landsberg among five families of metrics, in which the first two inclusions are known to be proper by virtue of ...
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 کاملOn 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 کاملThe Geometry of Finsler Spaces
The term "Finsler space " evokes in most mathematicians the picture of an impenetrable forest whose entire vegetation consists of tensors. The purpose of the present lecture is to show that the association of tensors (or differential forms) with Finsler spaces is due to an historical accident, and that, at least at the present time, the fruitful and relevant problems lie in a different directio...
متن کاملMedians and means in Finsler geometry
We investigate existence and uniqueness of p-means ep and the median e1 of a probability measure μ on a Finsler manifold, in relation with the convexity of the support of μ. We prove that ep is the limit point of a continuous time gradient flow. Under some additional condition which is always satisfied for p ≥ 2, a discretization of this path converges to ep. This provides an algorithm for dete...
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2006
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2006.04.005