We consider non-linear gravitational models with a multidimensional warped product geometry. Particular attention is payed to models with quadratic scalar curvature terms. It is shown that for certain parameter ranges, the extra dimensions are stabilized if the internal spaces have negative constant curvature. In this case, the 4–dimensional effective cosmological constant as well as the bulk c...

This article uses the Berwald connection exclusively, together with its two curvatures, to cut an efficient path across the landscape of Finsler geometry. Its goal is to initiate differential geometers into two key research areas in the field: the search for unblemished “unicorns” and the study of Ricci flow. The exposition is almost self-contained.

Berwald and Wagner manifolds are two important classes of spaces in Finsler geometry. They are closely related to each other via the conformal change of the metric. After discussing the basic definitions and the elements of the theory we present general methods to construct examples of them.

The Cosmic no hair theorem is studied in anisotropic Bianchi brane models which admit power law inflation with a scalar field. We note that all Bianchi models except Bianchi type IX transit to an inflationary regime and the anisotropy washes out at a later epoch. It is found that in the brane world, the anisotropic universe approaches the isotropic phase via inflation much faster than that in t...

We obtain expressions for the vacuum expectations of the energy-momentum tensor of the scalar field with an arbitrary coupling to the curvature in an N-dimensional homogeneous isotropic space for the vacuum determined by diagonalization of the Hamiltonian. We generalize the n-wave procedure to N-dimensional homogeneous isotropic space-time. Using the dimensional regularization, we investigate t...

In the framework of supersymmetric tensors and multivariate homogeneous polynomials, the talk discusses the relevance of the spectral properties of the Berwald-Moor, Chernov and Bogoslovski multilinear forms, towards the underlying geometry of the locally-Minkovski Finsler associated structures, which have been intensively investigated as promising candidate models for Special Relativity Theory...

We introduced a class of conformally invariant Ehresmann connections so–called L-horizontal endomorphism in [7]. Using this class, we define conformally invariant manifolds: Wagner–type manifold and locally Minkowski–type manifold as special generalized Berwald manifolds. Then a generalization of Hashiguchi–Ichijyō’s Theorems to Wagner–type manifolds is presented. Mathematics Subject Classifica...