Related papers: Webs and projective structures on a plane
This paper deals with the problem of describing the vector spaces of divergence-free, natural tensors on a pseudo-Riemannian manifold that are second-order; i.e., that are defined using only second derivatives of the metric. The main result…
For a four-dimensional (nonisoclinicly geodesic) three-web W (3, 2, 2), a transversal distribution $\Delta$ is defined by the torsion tensor of the web. In general, this distribution is not integrable. The authors find necessary and…
We classify all closed 1-connected manifolds $M$ which look like projective planes, i.e. with integral homology $H_*(M)=Z^3$. Furthermore, we give an explicit construction of these manifolds as Thom spaces of open disk bundles.
We present old and recent results on rank problems and linearizability of geodesic planar webs.
A projective rectangle is like a projective plane that may have different lengths in two directions. We develop properties of the graph of lines, in which adjacency means having a common point, especially its strong regularity and clique…
In this paper we contribute towards the classification of partially symmetric tensors in $\mathbb{F}_q^3\otimes S^2\mathbb{F}_q^3$, $q$ even, by classifying planes which intersect the Veronese surface $\mathcal{V}(\mathbb{F}_q)$ in at least…
We derive necessary conditions for a complex projective structure on a complex surface to arise via the Levi-Civita connection of a (pseudo-)K\"ahler metric. Furthermore we show that the (pseudo-)K\"ahler metrics defined on some domain in…
In a series of recent papers, we have introduced an object that was constructed on the connection but which was proven to be a tensor: this object, thus called tensorial connection, has been defined and some of its properties have been…
We describe 4th order ODEs satisfying two contact invariant conditions of Bryant in terms of the Ricci tensor of a certain gl(2,R) valued connection. We also provide nonhomogeneous examples of such ODEs.
We derive a closed-form expression for the projection onto a capped rotated second-order cone -- a convex set that arises in perspective relaxations of nonlinear programs with binary indicator variables. The closed-form solution involves…
The main objective of the present paper is to set up the theoretical basis and the language needed to deal with the problem of direct images of hermitian vector bundles for projective non-necessarily smooth morphisms. To this end, we first…
We find certain relations between flag Hilbert schemes of points on plane curves and moduli spaces of one-dimensional plane sheaves. We show that some of these moduli spaces are unirational.
The aim of this paper is to construct a Riemann-Lagrange geometry on 1-jet spaces, in the sense of d-connections, d-torsions, d-curvatures, electromagnetic d-field and geometric electromagnetic Yang-Mills energy, starting from a given…
We examine questions of geometric realizability for algebraic structures which arise naturally in affine and Riemannian geometry. Suppose given an algebraic curvature operator R at a point P of a manifold M and suppose given a real analytic…
We introduce a notion of constructibility for \'etale sheaves with torsion coefficients over a suitable class of adic spaces. This notion is related to the classical notion of constructibility for schemes via the nearby cycles functor. We…
A projective link is a smooth closed 1-submanifold of the real projective space of dimension three. A projective link is said to be affine if it is isotopic to a link, which does not intersect some projective plane. The main result: a…
A new section on projections of coherent sheaves from a projective space to a lower-dimensional projective space has been added. Also some of the notation has been altered to bring it into line with the joint paper with Eisenbud and…
We present the foundations of a projective geometric theory of elasticity, as well as outline a few possible application possibilities. We give the description of the Cauchy stress and infinitesimal strain tensors compatible with coordinate…
In the literature different concepts of compatibility between a projective structure and a conformal structure on a differentiable manifold are used. In particular compatibility in the sense of Weyl geometry is slightly more general than…
In this work we investigate the transfer of fundamental order and completeness properties between truncated Riesz spaces and their unitizations. Specifically, we provide characterizations and equivalences for several notions of…