Related papers: Sections along maps in Geometry and Physics
On Sasakian manifolds with their naturally occurring sub-Riemannian structure, we consider parallel and mirror maps along geodesics of a taming Riemannian metric. We show that these transport maps have well-defined limits outside the…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
Extra dimensions can be utilized to simplify problems in classical mechanics, offering new insights. Here we show a simple example of how the motion of a test particle under the influence of an inverse-quadratic potential in 1D is…
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…
These notes explore some aspects of formal derived geometry related to classical field theory. One goal is to explain how many important classical field theories in physics -- such as supersymmetric gauge theories and supersymmetric…
We develop parallel transport on path spaces from a differential geometric approach, whose integral version connects with the category theoretic approach. In the framework of 2-connections, our approach leads to further development of…
In this paper a new supersymmetric extension of conformal mechanics is put forward. The beauty of this extension is that all variables have a clear geometrical meaning and the super-Hamiltonian turns out to be the Lie-derivative of the…
The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency…
While the interpretation of high-dimensional datasets has become a necessity in most industries, and is supported by continuous advances in data science and machine learning, the spatial visualization of higher-dimensional geometry has…
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…
The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A…
Motivated by the supersymmetric version of Dirac's theory, chiral models in field theory, and the quest of a geometric fundament for the Standard Model, we describe an approach to the differential geometry of vector bundles on…
A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…
These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
The geometrical (superembedding) approach is used as a tool for deriving from the worldvolume dynamics of superbranes field theoretical models exhibiting partial supersymmetry breaking. In this way we obtain nonlinear actions for Goldstone…
We reformulate superalgebra and supergeometry in completely categorical terms by a consequent use of the functor of points. The increased abstraction of this approach is rewarded by a number of great advantages. First, we show that one can…