A linear connection on a Finsler manifold is called compatible to the function if its parallel transports preserve Finslerian length of tangent vectors. Generalized Berwald manifolds are equipped with connection. In paper we present general and intrinsic method characterize connections dimension three. We prove that not unique then indicatrices must be Euclidean surfaces revolution. The surplus...

We study the stability of the isotropic vacuum Friedmann universe in gravity theories with higherorder curvature terms of the form (RabR ) added to the Einstein-Hilbert Lagrangian of general relativity on approach to an initial cosmological singularity. Earlier, we had shown that, when n = 1, a special isotropic vacuum solution exists which behaves like the radiation-dominated Friedmann univers...

Most of the observational claims in cosmology are based on the assumption that the universe is isotropic and homogeneous so they essentially test different types of Friedmann models. This also refers to recent observations of supernovae Ia, which, within the framework of Friedmann cosmologies give strong support to negative pressure matter and also weaken the age conflict. In this essay we drop...

In this work, the rectifying isotropic curves are investigated in three-dimensional complex space C3. The conclusion that an curve is a if and only its pseudo curvature linear function of arc-length achieved. Meanwhile, expressed by Bessel functions explicitly. Last but not least, centrodes explored detail.

When the interfacial energy is a nonconvex function of orientation, the anisotropic curvature flow equation becomes backward parabolic. To overcome the instability thus generated, a regularization of the equation that governs the evolution of the interface is needed. In this paper we develop a regularized theory of curvature flow in threedimensions that incorporates surface diffusion and bulk-s...

The growth of small perturbations and the temperature correlation function of cosmic background radiation induced by the perturbations in the isotropic and homogeneous universe with arbitrary spatial curvature, filled with nonrelativistic and so-called string-like matter is calculated. It is shown that both magnitudes are insensitive to the eventual existence of the string-like matter in the un...

The concept of locally dually flat Finsler metrics originate from information geometry. As we know, (α, β)-metrics defined by a Riemannian metric α and an 1-form β, represent an important class of Finsler metrics, which contains the Matsumoto metric. In this paper, we study and characterize locally dually flat first approximation of the Matsumoto metric with isotropic S-curvature, which is not ...

I discuss the possibility of using a massive vector field to generate the density perturbation in the Universe. I find that a scale-invariant superhorizon spectrum of vector field perturbations is possible to generate during inflation. The associated curvature perturbation is imprinted onto the Universe following the curvaton scenario. The mechanism does not generate a long-range anisotropy bec...

Within trie boundary-layer model and by taking into account only interface kinetics (isotropic or anisotropic), we find a contmuous set of « kinetic » dendrites. This solution exists at arbitrary supercooling A in the 2Dand 3D-axisymmetric cases and reduces to the usual dendrites with parabolic tails at A ~ l, and « angular » dendrites at A ~ l. In contrast with classical Ivantsov dendrites, th...