Related papers: Geometria nieortodoksyjna
This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau's special setting) and its applications to general relativity with a special focus on the distributional description of impulsive…
This survey is an invitation to recent developments in higher dimensional birational geometry.
It is a review of some results in Odd symplectic geometry related to the Batalin-Vilkovisky Formalism
The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.
Survey talk on certain aspects of the subject, stressing the neighbor relation as a basic notion in differential geometry.
This is a survey on coarse geometry with an emphasis on coarse homology theories.
Gravity with incorporation of additional dimensions and noncommutative geometry.
We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
A recently introduced canonical divergence $\mathcal{D}$ for a dual structure $(\mathrm{g},\nabla,\nabla^*)$ is discussed in connection to other divergence functions. Finally, open problems concerning symmetry properties are outlined.
A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…
The geometries of spaces having as groups the real orthogonal groups and some of their contractions are described from a common point of view. Their central extensions and Casimirs are explicitly given. An approach to the trigonometry of…
These are lecture notes for the course "Poisson geometry and deformation quantization" given by the author during the fall semester 2020 at the University of Zurich. The first chapter is an introduction to differential geometry, where we…
Geometrical structures intrinsic to non-expanding, weakly isolated and isolated horizons are analyzed and compared with structures which arise in other contexts within general relativity, e.g., at null infinity. In particular, we address in…
Symplectic and Poisson geometry emerged as a tool to understand the mathematical structure behind classical mechanics. However, due to its huge development over the past century, it has become an independent field of research in…
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…
This text consists on a series of introductory lectures on cosmology for mathematicians and physicists who are not specialized on the subject.
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
Lecture notes on Finsler Geometry
A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.