Intrinsic geometry of line congruences and their projective deformations

Discrete asymptotic nets and W-congruences in Plücker line geometry

The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plücker quadric. On the basis of the Lelieuvre-type representation of asymptotic lattices and of the discrete analog of the Moutard transformation, it is constructed the discrete analog of the W–congruences...

A note on deformations of bundles on the projective line

We determine in an elementary fashion the dimension of the space of innni-tesimal deformations of an arbitrary vector bundle on the complex projective line, showing its dependence on the precise form of the decomposition of the bundle under consideration.

Mirror Symmetry for Weighted Projective Planes and Their Noncommutative Deformations

Intrinsic Theory of Projective Changes in Finsler Geometry

The aim of the present paper is to provide an intrinsic investigation of projective changes in Finlser geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental projectively invariant tensors, namely, the projective deviation tensor, the Weyl ...

The Euclidean geometry deformations and capacities of their application to microcosm space - time geometry

Usually a Riemannian geometry is considered to be the most general geometry, which could be used as a space-time geometry. In fact, any Riemannian geometry is a result of some deformation of the Euclidean geometry. Class of these Riemannian deformations is restricted by a series of unfounded constraints. Eliminating these constraints, one obtains a more wide class of possible space-time geometr...