Related papers: Beltrami's theorem via parabolic geometry

Given a base point free linear system on an algebraic variety, many classes of singularities are stable under taking suitable members after enlarging the base field. We establish analogous results when the base ring is an excellent ring.

A slight modification to one of Tarski's axioms of plane Euclidean geometry is proposed. This modification allows another of the axioms to be omitted from the set of axioms and proven as a theorem. This change to the system of axioms…

We establish an analogue of the fundamental theorem of algebra for polynomial matrix equations, in which the matrices-coefficients and unknown matrix are assumed to be circulant matrices.

In this paper we prove an abstract theorem which can be used to study the existence of solitons for various dynamical systems described by partial differential equations. We also give an idea of how the abstract theorem can be applied to…

Using the symmetry properties of two-dmensional sigma models, we introduce a notion of the Beltrami-Courant differential, so that there is a natural homotopy Gerstenhaber algebra related to it. We conjecture that the generalized…

We consider the question raised by Enciso and Peralta-Salas in [4] (see arXiv:1402.6825): What nonconstant functions $f$ can occur as the proportionality factor for a Beltrami field $\mathbf{u}$ on an open subset $U \subset \mathbb{R}^3$?…

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.

In this article using elementary school level Geometry we observe an alternative proof of Pythagorean Theorem from Heron's Formula.

A mechanism for the inheritance of properties of spectra by differential spectra is developed and applied to prove geometric properties of morphisms of differential algebraic varieties.

We show that a single special separation theorem (namely, a consequence of the geometric form of the Hahn-Banach theorem) can be used to prove Farkas type theorems, existence theorems for numerical quadrature with positive coefficients, and…

We generalize the concept of affine locally symmetric spaces for parabolic geometries. We discuss mainly $|1|$--graded geometries and we show some restrictions on their curvature coming from the existence of symmetries. We use the theory of…

Using fundamental results of Deligne, we prove a nilpotence theorem for algebraic cycles and use this to prove a torsion nilpotence result for correspondences on surfaces.

We consider the equation rotB+aB=0 (1) in the plane with a being a real-valued function and show that it can be reduced to a Vekua equation of a special form. In the case when a depends on one Cartesian variable a complete system of exact…

We present a rectilinearization theorem for p-adic semi-algebraic sets depending on parameters. As an application of our main theorem we present an alternative proof of a rationality result for parametric p-adic inte- grals, due to Denef.

A new simple way to prove the Frobenius conjecture on the dimensions of real algebras without zero divisors is given.

Galois theory is developed using elementary polynomial and group algebra. The method follows closely the original prescription of Galois, and has the benefit of making the theory accessible to a wide audience. The theory is illustrated by a…

The aim of this note is to provide an intrinsic proof of the Gauss--Bonnet theorem without invoking triangulations, which is achieved by exploiting complex structures.

In this paper, the geometric approach to the virial theorem developed in \cite{CFR12} is written in terms of quasi-velocities (see \cite{CNCS07}). A generalization of the virial theorem for mechanical systems on Lie algebroids is also…

A vector field is called a Beltrami vector field, if $B\times(\nabla\times B)=0$. In this paper we construct two unique Beltrami vector fields $\mathfrak{I}$ and $\mathfrak{Y}$, such that $\nabla\times\mathfrak{I}=\mathfrak{I}$,…

We describe all pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta. As an application, we solve the Beltrami problem on closed surfaces, prove the nonexistence of…