The notion of isometric submersion is extended to Finsler spaces and it is used to construct examples of Finsler metrics on complex and quaternionic projective spaces all of whose geodesics are (geometrical) circles.

In 1977, M. Matsumoto and R. Miron [9] constructed an orthonormal frame for an n-dimensional Finsler space, called ‘Miron frame’. The present authors [1, 2, 3, 10, 11] discussed four-dimensional Finsler spaces equipped with such frame. M. Matsumoto [7, 8] proved that in a three-dimensional Berwald space, all the main scalars are h-covariant constants and the h-connection vector vanishes. He als...

In this paper we obtain the conditions in which two complex Finsler metrics are projective, i.e. have the same geodesics as point sets. Two important classes of such metrics are submitted to our attention: conformal projective and weakly projective complex Finsler spaces. For each of them we study the transformations of the canonical connection. We pay attention for local projectivity with a pu...

We study the asymptotics of number $N(t)$ geometrically distinct closed geodesics length $\leq t$ a Riemannian or Finsler metric on connected sum two compact manifolds dimension at least three with non-trivial fundamental groups, and apply results to prime decomposition three-manifold. In particular we show that function grows like numbers $3$-manifold infinite group. It follows generic has inf...

We first present the natural definitions of horizontal differential, divergence (as an adjoint operator), and a $p$-harmonic form on Finsler manifold. Next, we prove Hodge-type theorem for manifold in sense that $p$-form is harmonic if only Laplacian vanishes. This viewpoint provides new appropriate definition vector fields geometry. approach leads to Bochner-Yano type classification based Ricc...

In this paper we introduce the class of R-complex Finsler spaces with (α, β)-metrics and study some important exemples: R-complex Randers spaces, R-complex Kropina spaces. The metric tensor field of a R-complex Finsler space with (α, β)-metric is determined (§2). A special approach is dedicated to the R-complex Randers spaces (§3). AMS Mathematics Subject Classification (2000): 53B40, 53C60

The starting point of the famous structure theorems on Berwald spaces due to Z.I. Szabó [4] is an observation on the Riemann-metrizability of positive definite Berwald manifolds. It states that there always exists a Riemannian metric on the underlying manifold such that its Levi-Civita connection is just the canonical connection of the Berwald manifold. In this paper we present a new elementary...

In this paper, we study the distributions and affine of quantum mechanical system. Also, discuss controllability system with related question concerning minimum time needed to steer a from unitary evolution $U(0)=I$ propagator desired $U_f$. Furthermore, paper introduces description $\mathfrak{k} \oplus \mathfrak{p}$ sub-Finsler manifold its geodesics, which equivalents problem driving an arbit...

This paper is concerned with a symbolic-based synthesis of feedback control policies for hybrid and continuous dynamic systems. A key step in our synthesis procedure is a new method to solve the following dynamic programming problem: ∂V ∂t (z, t) = min v ∂V ∂z (z, t)ρv(z, v)v ż = ρ(z, v), t ∈ [0, T ] (1) V (z, T ) = Ψ(z, T ) (2) Here V (z, t) is the cost-to-go function associated with a certain...

The compactness theorem of Galloway is a stronger version of the Bonnet-Myers theorem allowing the Ricci scalar to take also negative values from a set of real numbers which is bounded below. In this paper we allow any negative value for the Ricci scalar, and adding a condition on its average, we find again that the manifold is compact and provide an upper bound of its diameter. Also, with no c...