相关论文: Sub-Riemannian geometry and Lie groups. Part I

This text is an introductory review of the basic concepts of the theory of semi-Riemannian geometry on real finite-dimensional manifolds without boundary.

This document is the first iteration of an attempt to collate information about small-rank groups of Lie type over small fields, and their representation theory over the defining field. This information is important in the author's work on…

The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several aspects of this correspondence. At the…

These are notes of a graduate course on representations of non-compact semisimple Lie groups given by the author at MIT.

Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. This branch of differential geometry is still so far from being exhausted; only a small portion of an…

These notes form an introduction to Lie algebras and group theory. Most of the material can be found in many works by various authors given in the list of references. The reader is referred to such works for more detail.

This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…

These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.

A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…

This is a survey article with a limited list of references (as required by the publisher) which appears in the Encyclopedia of Mathematical Physics, eds. J.-P. Francoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006. vol.4, pp.94--104.

This is the introduction and bibliography for lecture notes of a course given at the Summer School on Noncommutative Geometry and Applications, sponsored by the European Mathematical Society, at Monsaraz and Lisboa, Portugal, September…

This is an essay to accompany the author's lecture at the introductory workshop on `Nonabelian fundamental groups in arithmetic geometry' at the Newton Institute, Cambridge in July, 2009.

This thesis is about the study of Lie groupoids endowed with a compatible (multiplicative) differential 1-form. The motivation and scope of the present work is to study the geometry of PDEs using the formalism of Lie groupoids and…

These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous…

We study sub-Riemannian and sub-Lorentzian geometry on the Lie group $\SU(1,1)$ and on its universal cover $\CSU(1,1)$. In the sub-Riemannian case we find the distance function and completely describe sub-Riemannian geodesics on both…

We give the complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. This classifications recovers other known classification results in the…

The Golden Ratio is fascinating topic that continually generated news ideas. A Riemannian manifold endowed with a Golden Structure will be called a Golden Riemannian manifold. The main purpose of the present paper is to study the geometry…

We develop the structure theory of symplectic Lie groups based on the study of their isotropic normal subgroups. The article consists of three main parts. In the first part we show that every symplectic Lie group admits a sequence of…

The unit sphere $\mathbb S^3$ can be identified with the unitary group SU(2). Under this identification the unit sphere can be considered as a non-commutative Lie group. The commutation relations for the vector fields of the corresponding…

The present volume is the written version of the series of lectures the author delivered at the Catholic University of Leuven, Belgium during the period of June-July, 1990. The main purpose of these talks is to present some of author's work…