Related papers: On Isomorphisms of Grassmann Spaces

We prove two conjectures on weighted complete intersections and give the complete classification of threefold weighted complete intersections in weighted projective space that are canonically or anticanonically embedded.

In this paper we characterize off-diagonal Carleson embeddings for both Hardy-Orlicz spaces and Bergman-Orlicz spaces of the upper-half plane. We use these results to obtain embedding relations and pointwise multipliers between these…

The purpose of this article is to investigate the relationship between suborbifolds and orbifold embeddings. In particular, we give natural definitions of the notion of suborbifold and orbifold embedding and provide many examples.…

We extend the concept of graph isomorphisms to multilayer networks with any number of "aspects" (i.e., types of layering). In developing this generalization, we identify multiple types of isomorphisms. For example, in multilayer networks…

Generalization of the cross ratio to polarizations of linear finite and infinite-dimensional spaces (in particular to Sato Grassmannian) is given and explored. This cross ratio appears to be a cocycle of the canonical (tautalogical) bundle…

We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.

Some geometric structures with associated Riemannian metrics have been considered in the book.

We study holomorphic isometries between bounded symmetric domains with respect to the Bergman metrics up to a normalizing constant. In particular, we first consider a holomorphic isometry from the complex unit ball into an irreducible…

We report on results about a study of algebraic graph invariants, based on computer exploration, and motivated by graph-isomorphism and reconstruction problems.

This is part one of a series of papers. In this series of papers, we consider problems analogous to the Oppenheim conjecture from the viewpoint of prehomogeneous vector spaces.

We apply a symmetrization procedure to the setting of Jacobi expansions and study potential spaces in the resulting situation. We prove that the potential spaces of integer orders are isomorphic to suitably defined Sobolev spaces. Among…

A class of trigonometric interpolation splines depending on parameter vectors, selected convergence factors and interpolation factors is considered. The concept of crosslink grids and interpolation grids is introduced; these grids can match…

We investigate the geometric and topological structure of equidistant decompositions of Riemannian manifolds.

In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.

The object of this article is to compute the holonomy group of the normal connection of complex parallel submanifolds of the complex projective space. We also give a new proof of the classification of complex parallel submanifolds by using…

Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of…

This article describes the symmetries of plane wave spacetimes in dimension four and greater. It begins with a description of the isometric automorphisms, and in particular the homogeneous plane waves. Then the article turns to describing…

We construct an explicit de Rham isomorphism relating the cohomology rings of Banagl's de Rham and spatial approach to intersection space cohomology for stratified pseudomanifolds with isolated singularities. Intersection space…

In this paper, we study the complex Landsberg spaces and some of their important subclasses. We introduce and characterize the class of generalized Berwald and complex Landsberg spaces. The intersection of these spaces gives the so called…

We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relation with Gromov--Witten theory and integrable systems.