Related papers: Two Fefferman-type constructions involving almost …
Given a finite Lie incidence geometry which is either a polar space of rank at least $3$ or a strong parapolar space of symplectic rank at least $4$ and diameter at most $4$, or the parapolar space arising from the line Grassmannian of a…
In his book "Metric structures for Riemannian and non-Riemannian spaces", Gromov defined two properties of Riemannian manifolds, ellipticity and quasiregular ellipticity, and suggested that there may be a connection between the two. Since…
This thesis concerns embeddings and self-embeddings of foundational structures in both set theory and category theory. The first part of the work on models of set theory consists in establishing a refined version of Friedman's theorem on…
It is shown that the fermionic Heisenberg-Weyl algebra with 2N=D fermionic generators is equivalent to the generalized Grassmann algebra with two fractional generators. The 2,3 and 4 dimensional Heisenberg - Weyl algebra is explicitly given…
We present a geometric construction and characterization of $2n$-dimensional split-signature conformal structures endowed with a twistor spinor with integrable kernel. The construction is regarded as a modification of the conformal…
This paper is a continuation of Part I where the general setup was developed. Here we discuss the general equivalence problem for geometric structures and provide criteria for the equivalence, local and global, of transitive structures.…
We elaborate an unified geometric approach to classical mechanics, Riemann-Finsler spaces and gravity theories on Lie algebroids provided with nonlinear connection (N-connection) structure. There are investigated the conditions when the…
We introduce an alternative description of coarse proximities. We define a coarse normality condition for connected coarse spaces and show that this definition agrees with large scale normality defined in [3] and asymptotic normality…
We classify quasilinear systems in Riemann invariants whose characteristic webs are linearizable on every solution. Although the linearizability of an individual web is a rather nontrivial differential constraint, the requirement of…
We generalize the adjunction between the functors $Rf_*$ and $f^!$ of derived categories of quasi-coherent sheaves for proper morphisms $f\colon X \to Y$ of Noetherian schemes to the following situation: Let $f$ be a finite type morphism…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
In this paper, we prove a theorem that gives a simple criterion for generating commuting pairs of generalized almost complex structures on spaces that are the product of two generalized almost contact metric spaces. We examine the…
The Gauss map of a projective variety $X \subset \mathbb{P}^N$ is a rational map from $X$ to a Grassmann variety. In positive characteristic, we show the following results. (1) For given projective varieties $F$ and $Y$, we construct a…
We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra. We describe derivations, differential operators, differential…
We show that when $d \geq 3$, the Hilbert scheme $Hilb_{dT+1-\binom{d-1}{2}}(G(k,n))$ has 2 components, even though elements in both components have the same cohomology class. Moreover, we show that the Hilbert scheme associated to the…
We introduce an extension of the fellow traveler property which allows fellow travelers to be at distance bounded from above by a function $f(n)$ growing slower than any linear function. We study normal forms satisfying this extended fellow…
In this paper, we define and study strong right-invariant sub-Riemannian structures on the group of diffeomorphisms of a manifold with bounded geometry. We derive the Hamiltonian geodesic equations for such structures, and we provide…
For more than hundred years, various concepts were developed to understand the fields of geometric objects and invariant differential operators between them for conformal Riemannian and projective geometries. More recently, several general…
The class W_1 of conformal Riemannian P-manifolds is the largest class of Riemannian almost product manifolds, which is closed with respect to the group of the conformal transformations of the Riemannian metric. This class is an analogue of…
We provide a manifestly topological classification scheme for generalised Weyl semimetals, in any spatial dimension and with arbitrary Weyl surfaces which may be non-trivially linked. The classification naturally incorporates that of Chern…