Related papers: Introduction to exterior differential systems
These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.
We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of such an exterior differential system. We support our…
We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these…
This primer is intended as an introduction to differential forms, a central object in modern mathematical physics, for scientists and engineers.
This is an elementary introduction to exterior differential systems motivated by two examples: minimal submanifolds and the isometric embedding problem. The two main goals of the lectures are: 1. To explain how to find an appropriate…
Short introduction to exotic differential structures on manifolds is given. The possible physical context of this mathematical curiosity is discussed. The topic is very interesting although speculative.
We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential…
This book is a textbook for the basic course of differential geometry. It is recommended as an introductory material for this subject.
This is a draft of a textbook on differential forms. The primary target audience is sophmore level undergraduates enrolled in what would traditionally be a course in vector calculus. Later chapters will be of interest to advaced…
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information…
These are expository notes from the 2008 Srni Winter School. They have two purposes: (1) to give a quick introduction to exterior differential systems (EDS), which is a collection of techniques for determining local existence to systems of…
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
This is a brief pedagogical introduction to the theory of large deviations. It appeared in the ICTS Newsletter 2017 (Volume 3, Issue 2), goo.gl/pZWA6X.
This is an introductory article to the theory of multiple gaps.
A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
This article provides a gentle, visual introduction to the basic concepts of differential geometry appropriate for students familiar with special relativity. Visual methods are used to explain basics of differential geometry and build…
An exposition of the basic geometry of twistor integrals, intended for mathematicians.