Differential and Riemannian geometry

With each methodology treated in its own chapter, this monograph is a thorough exploration of several theories that can be used to find explicit formulas for heat kernels for both elliptic and sub-elliptic operators.

The subjects of stochastic processes, information theory, and Lie groups are usually treated separately from each other.

The subjects of stochastic processes, information theory, and Lie groups are usually treated separately from each other.

The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry.

Advances in technology over the last 25 years have created a situation in which workers in diverse areas of computerscience and engineering have found it neces- sary to increase their knowledge of related fields in order to make further progress.

Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase.

Geometric measure theory has roots going back to ancient Greek mathematics, for considerations of the isoperimetric problem (to ?

Differential geometry, in the classical sense, is developed through the theory of smooth manifolds.

Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities.

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries.

This book is an outgrowth of the special term "e;Harmonic Analysis, Representation Theory, and Integral Geometry,"e; held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics in Bonn during the summer of 2007.

This book introduces geometric spectral theory in the context of Riemann surfaces.

This volume uses a unified approach to representation theory and automorphic forms.

Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory.

This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics.

Riemannian Topology and Geometric Structures on Manifolds results from a similarly entitled conference held at the University of New Mexico in Albuquerque.

Hideki Omori is widely recognized as one of the world's most creative and original mathematicians.

This text presents differential forms from a geometric perspective accessible at the undergraduate level.

This monograph presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology.

The study of CR manifolds lies at the intersection of three main mathematical disciplines, partial differential equations: complex analysis in several complex variables, and differential geometry.

This research monograph is a systematic exposition of the background, methods, and recent results in the theory of cycle spaces of ?

Differential geometry, in the classical sense, is developed through the theory of smooth manifolds.

Complex variables is a precise, elegant, and captivating subject.

Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces, a self-contained work by A.

Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics.

This volume contains research and survey articles by well known and respected mathematicians describing recent developments and research trends in differential geometry and topology that have been collected and dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields.

Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics.

One of the world's foremost geometers, Alan Weinstein has made deep contributions to symplectic and differential geometry, Lie theory, mechanics, and related fields.

This concise guide to the differential geometry of curves and surfaces can be recommended to ?

Applications covered include image segmentation, shape analysis, image enhancement, and tracking.

Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry.

This little book is especially concerned with those portions of "e;advanced calculus"e; in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.

A readable introduction to the subject of calculus on arbitrary surfaces or manifolds.

This little book is especially concerned with those portions of "e;advanced calculus"e; in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.

A readable introduction to the subject of calculus on arbitrary surfaces or manifolds.

Differential Geometry of Manifolds, Second Edition presents the extension of differential geometry from curves and surfaces to manifolds in general.

Differential Geometry of Manifolds, Second Edition presents the extension of differential geometry from curves and surfaces to manifolds in general.

Comprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress.

Although twistor theory originated as an approach to the unification of quantum theory and general relativity, twistor correspondences and their generalizations have provided powerful mathematical tools for studying problems in differential geometry, nonlinear equations, and representation theory.

This self-contained text is an excellent introduction to Lie groups and their actions on manifolds.

This book provides a modern treatment of Lie's geometry of spheres, its applications and the study of Euclidean space.

This book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to the study of some problems considered in nonlinear analysis, in geometry, and in applied mathematics.

Differential forms satisfying the A-harmonic equations have found wide applications in fields such as general relativity, theory of elasticity, quasiconformal analysis, differential geometry, and nonlinear differential equations in domains on manifolds.

This book offers the most comprehensive survey to date of the theory of semiparallel submanifolds.

Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups.

"e;From nothing I have created a new different world,"e; wrote Janos Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today.

Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry.