Related papers: Lie applicable surfaces
The method of moving frames in Lie sphere geometry has produced significant results in the classification of Dupin hypersurfaces in spheres. What is the secret of its effectiveness? The answer emerges in the classification of nonumbilic…
In this paper, we apply the moving plane method to some degenerate elliptic equations to get a Liouville type theorem. As an application, we derive the a priori bounds for positive solutions of some semi-linear degenerate elliptic…
We provide a convincing discretisation of Demoulin's $\Omega$-surfaces along with their specialisations to Guichard and isothermic surfaces with no loss of integrable structure.
The main aim of this paper is to introduce a new version of the Fokas-Gel'fand formula for immersion of soliton surfaces in Lie algebras. The paper contains a detailed exposition of the technique for obtaining exact forms of 2D-surfaces…
We consider the gauge transformations of a metric $G$-bundle over a compact Riemannian surface with boundary. By employing the heat flow method, the local existence and the long time existence of generalized solution are proved.
We study the representation theory of finite-dimensional $\omega$-Lie algebras over the complex field. We derive an $\omega$-Lie version of the classical Lie's theorem, i.e., any finite-dimensional irreducible module of a soluble…
We develop a theory of Lie algebroids over differentiable stacks that extends the standard theory of Lie algebroids over manifolds. In particular we show that Lie algebroids satisfy descent for submersions, define the category of Lie…
This paper contains some results about Teichm\"uller spaces of non-orientable surfaces (Klein surfaces). We prove several theorems giving isomorphisms between deformation spaces of Klein surfaces. These results show the similarity between…
We introduce orbifold Euler numbers for normal surfaces with Q-divisors. These numbers behave multiplicatively under finite maps and in the log canonical case we prove that they satisfy the Bogomolov-Miyaoka-Yau type inequality. As a…
In this work we deal with coverings and actions of Lie group- groupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids.…
The local symmetry transformations of the quantum effective action for general gauge theory are found. Additional symmetries arise under consideration of background gauges. Together with "trivial" gauge transformations, vanishing on mass…
We give a convenient reformulation, a slight generalization and some applications of the formality transfer theorem for DG-Lie algebras.
This is the English translation of Leonhard Euler's Latin paper "De solidis quorum superficiem in planum explicare licet". Euler explains several methods to obtain equations for developable surfaces. Therefore, this paper might be…
In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus. It turns out that the relevant algebraic…
We remark some basic facts on homological aspects of involutive Lie bialgebras and their involutive bimodules, and present some problems on surface topology related to these facts.
We prove a strong analogue of Liouville's Theorem in Diophantine approximation for points on arbitrary algebraic varieties. We use this theorem to prove a conjecture of the first author for cubic surfaces in $\P^3$.
This paper is devoted to the development and applications of some (new) basic concepts in Lie theory, both from `computational" and "observability" viewpoint. We specify set of all "G-equivariant" maps from a given Lie group G to the…
We use the square peg problem for smooth curves to prove a generalized table Theorem for real valued functions on Riemannian surfaces with odd Euler characteristic. We then use this result to prove the table conjecture for even functions on…
We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie algebras and a homomorphism between them.
We discuss natural transformations in the context of Lie groupoids, and their infinitesimal counterpart. Our main result is an integration procedure that provides smooth natural transformations between Lie groupoid morphisms.