The theory of locally anisotropic superspaces (supersymmetric generalizations of various types of Kaluza–Klein, Lagrange and Finsler spaces) is laid down. In this framework we perform the analysis of construction of the supervector bundles provided with nonlinear and distinguished connections and metric structures. Two models of locally anisotropic supergravity are proposed and studied in detai...

A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in their turn, can be equivalently represented as almost Kähler spaces. This allows us to formulate an approach to quantum gravity following standard methods of deforma...

The (n+1)-dimensional Einstein-Gauss-Bonnet (EGB) model is considered. For diagonal cosmological metrics the equations of motion are written as a set of Lagrange equations with the Lagrangian containing two “minisuperspace” metrics on R : a 2-metric of pseudo-Euclidean signature and a Finslerian 4-metric that is proportional to n-dimensional Berwald-Moor 4-metric. When a synchronous time variab...

The mesh adaptation is a classical method for accelerating and improving the PDE finite element computation. Two tools are generally used: the metric [10] to define the mesh size and the error indicator to know if the solution is accurate enough. A lot of algorithms used to generate adapted meshes suitable for a PDE numerical solution for instance [15, 1] for discrete metrics, or [15, 2] for th...

We survey the geometry of Lagrange and Finsler spaces and discuss the issues related to the definition of curvature of nonholonomic manifolds enabled with nonlinear connection structure. It is proved that any commutative Riemannian geometry (in general, any Riemann– Cartan space) defined by a generic off–diagonal metric structure (with an additional affine connection possessing nontrivial torsi...

In the present paper we submit for study a new class of Finsler spaces. Through restricting the homogeneity condition from the definition of a complex Finsler metric to real scalars, λ ∈ R, is obtained a wider class of complex spaces, called by us the R−complex Finsler spaces. Two subclasses are taken in consideration: the Hermitian and the non-Hermitian R−complex Finsler spaces. In an R−comple...

A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in their turn, can be equivalently represented as almost Kähler spaces. This allows us to formulate an approach to quantum gravity following standard methods of deforma...

Munteanu (Complex spaces in Finsler, Lagrange and Hamilton Geometries, Kluwer Academic Publishers, Dordrecht, 2004) defined the canonical connection associated to a strongly pseudoconvex complex Finsler manifold (M, F). We first prove that holomorphic sectional curvature tensors of coincide with those Chern–Finsler F if only is Kähler-Finsler metric. also investigate relationship Ricci curvatur...

Lossy compression of motion capture data can alleviate the problems of efficient storage and transmission by exploiting the redundancy and the superfluous precision of the data. When considering the acceptable amount of distortion, perceptual issues have to be taken into account. Current state of the art methods reduce the data rate required for high quality storage of motion capture data using...