In this paper, it is elaborated the theory the Ricci flows for manifolds enabled with nonintegrable (nonholonomic) distributions defining nonlinear connection structures. Such manifolds provide a unified geometric arena for nonholonomic Riemannian spaces, Lagrange mechanics, Finsler geometry, and various models of gravity (the Einstein theory and string, or gauge, generalizations). We follow th...

We present a continuous and convex formulation for Finsler active contours using seed regions or utilizing a regional bias term. The utilization of general Finsler metrics instead of Riemannian metrics allows the segmentation boundary to favor appropriate locations (e.g. with strong image discontinuities) and suitable directions (e.g. aligned with dark to bright image gradients). Strong edges a...

here, the concept of electric capacity on finsler spaces is introduced and the fundamentalconformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact finslermanifold is conformal invariant. this work enables mathematicians and theoretical physicists to become morefamiliar with the global finsler geometry and one of its new 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.

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

A tangent manifold is a pair (M, J) with J a tangent structure (J2 = 0, ker J = im J) on the manifold M . A systematic study of tangent manifolds was done by I. Vaisman in [5]. One denotes by HM any complement of im J := TV . Using the projections h and v on the two terms in the decomposition TM = HM ⊕TV one naturally defines an almost complex structure F on M . Adding to the pair (M, J) a Riem...

The objective of this article is to build up a general theory of geometrical optics for spinning light rays in an inhomogeneous and anisotropic medium modeled on a Finsler manifold. The prerequisites of local Finsler geometry are reviewed together with the main properties of the Cartan connection used in this work. Then, the principles of Finslerian spinoptics are formulated on the grounds of p...

We generalize to the Finsler case, the Lelong-Ferrand-Obatta Theorem about the compactness of conformal groups of compact Riemannian manifolds, except, the standard sphere.

Abstract Finsler geometry is a natural arena to investigate the physics of spacetimes with local Lorentz violation. The directional dependence metric provides way encode Lorentz-violating effects into geometric structure spacetime. Here, classical field theory proposed in special geometry, so-called Randers-Finsler spacetime, where violation produced by background vector field. By promoting dif...

Following an introduction to control theory, we show how Finsler geometries occur in certain classes of control systems.