Related papers: On The Equivalence Problem for Geometric Structure…

The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…

Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a very difficult problem with many applications. While it is hopeless to expect much in general, we know a surprising amount about these…

This work is a spin-off of an on-going programme which aims at revisiting the original studies of Lie and Cartan on pseudogroups and geometric structures from a modern perspective. We encode geometric structures induced by transitive Lie…

I review some of my recent work on non-lorentzian geometry. I review the classification of kinematical Lie algebras and their associated Klein geometries. I then describe the Cartan geometries modelled on them and their characterisation in…

The author surveys the problem of piecing together integral or rational solutions to Diophantine equations (global structure) from solutions modulo congruences and real solutions (local structure).

A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with,…

We clarify the notion of effective equivalence and characterize geometrically the effectively equivalent permutation groups. In particular, we present examples showing that the latter do not correspond to affinely equivalent polytopes…

Shortened abstract: Given a constrained minimization problem, under what conditions does there exist a related, unconstrained problem having the same minimum points? This basic question in global optimization motivates this paper, which…

Starting with assumptions both simple and natural from "physical" point of view we present a direct construction of transformations preserving wide class of (anti)commutation relations which describe Euclidean/Minkowski superspace…

We use a well known problem in discrete and computational geometry (partitions of measures by $k$-fans) as a motivation and as a point of departure to illustrate many aspects, both theoretical and computational, of the problem of…

The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…

This is a survey of our research on geometric structures of projective embeddings and includes some topics of our talks in several symposia during 1990-99. We clarify our main problem, which is to construct a kind of geometric composition…

We study the equivariant real structures on complex horospherical varieties, generalizing classical results known for toric varieties and flag varieties. In particular, we obtain a necessary and sufficient condition for the existence of…

We provide five examples of conformal geometries which are naturally associated with ordinary differential equations (ODEs). The first example describes a one-to-one correspondence between the Wuenschmann class of 3rd order ODEs considered…

For a partial lattice L the so-called two-point extension is defined in order to extend L to a lattice. We are motivated by the fact that the one-point extension broadly used for partial algebras does not work in this case, i.e. the…

We present a brief review of physical problems leading to indefinite Hilbert spaces and non-hermitian Hamiltonians. With the exception of pseudo-Riemannian manifolds in GR, the problem of a consistent physical interpretation of these…

Following Thurston's geometrisation picture in dimension three, we study geometric manifolds in a more general setting in arbitrary dimensions, with respect to the following problems: (i) The existence of maps of non-zero degree (domination…

The problem is posed of further extending the axiomatic construction proposed in Part 1 for non-local point transformations mapping in each other different curved space times. The new transformations apply to curved space times when…

In this paper the notion of Dirac structure in finite dimension is extended to the convenient setting. In particular, we introduce the notion of partial Dirac structure on convenient Lie algebroids and manifolds. We then look for those…

This is a version of a part of the book ``Transformations of Grassman Spaces'' (in progress). We study transformations of Grassman spaces preserving certain geometrical constructions related to buildings. The next part will be devoted to…