相关论文: Transformations of Grassman Spaces
In a projective space we fix some set of points, a horizon, and investigate the complement of that horizon. We prove, under some assumptions on the size of lines, that the ambient projective space, together with its horizon, both can be…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
We study evolutes and involutes of space curves. Although much of the material presented is not new and can be found in classic treatises, we believe that a modern and unified treatment, complemented with several novel observations, may be…
In this paper we consider partial linear spaces induced on the point set of a polar space, but with as lines the hyperbolic lines of this polar space. We give some geometric characterizations of these and related spaces. The results have…
In this survey we give a brief introduction to, and review the progress made in the last decade in understanding the geometry of the moduli spaces A_g of principally polarized abelian varieties and its compactifications. Topics surveyed…
We introduce a class of Radon transforms for reductive symmetric spaces, including the horospherical transforms, and study some of their properties. In particular we obtain a support theorem that generalizes Helgason's support theorem for…
Lecture notes on Finsler Geometry
Conformal and disformal transformations are now being very intensively studied in the context of various modified gravity theories. In particular, some special classes of them can be used for constructing Mimetic Dark Matter models.…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
We explore the evolutionary behaviors of compact objects in a modified gravitational theory with the help of structure scalars. Particularly, we consider the spherical geometry coupled with heat and radiation emitting shearing viscous…
A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those…
This work contributes to the analysis of linear geometric polygon transformations with the aim to force a desired shape by an iterative procedure.
This paper studies compactifications of moduli spaces involving closed Riemann surfaces. The first main result identifies the homeomorphism types of these compactifications. The second main result introduces orbicell decompositions on these…
This paper is a continuation of our study of degenerations of Grassmannians in our last paper, called linked Grassmannians, constructed using convex lattice configurations in Bruhat-Tits buildings. We describe the geometry and topology of…
To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is…
This work explores the space of foliations on projective spaces over algebraically closed fields of positive characteristic, with a particular focus on the codimension one case. It describes how the irreducible components of these spaces…
This is a short introduction to affine and convex spaces, written especially for physics students. It summarizes different elementary presentations available in the mathematical literature, and blends analytic- and geometric-flavoured…
We describe the gauge-theoretic approach to transformations in integrable geometry through discussion of two classical examples: surfaces of constant negative Gauss curvature and isothermic surfaces. These are purely expository notes…
We construct a one parameter family of integral transforms connecting the classical Hardy space with a class of weighted Bergman spaces called Barut-Girardello spaces.
A priori, the set of birational transformations of an algebraic variety is just a group. We survey the possible algebraic structures that we may add to it, using in particular parametrised family of birational transformations.