Differential and Riemannian geometry

An accessible introduction to the intersection theory of punctured holomorphic curves and its applications in topology.

Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications.

Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications.

Represents the state of the art in the new field of synthetic differential topology.

With detailed explanations and numerous examples, this textbook covers the differential geometry of surfaces in Euclidean space.

Concise and modern introduction to differential topology with a hands-on approach and plentiful examples and exercises.

With detailed explanations and numerous examples, this textbook covers the differential geometry of surfaces in Euclidean space.

Concise and modern introduction to differential topology with a hands-on approach and plentiful examples and exercises.

The second volume in a series exploring the mathematics of aperiodic order.

An exposition of the theory of curves over a finite field, and connections to the Riemann Hypothesis for function fields.

An exposition of the theory of curves over a finite field, and connections to the Riemann Hypothesis for function fields.

This book is an elementary introduction to the geometrical methods and notions used in special and general relativity.

A comprehensive text and reference on sub-Riemannian and Heisenberg manifolds using a novel and robust variational approach.

Original research and expert surveys on Riemann surfaces.

An up-to-date survey of research in singularity theory.

This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry.

This book contains papers given at the International Singularity Conference held in 1991 at Lille.

This 1990 collection of review articles covers the considerable progress made in a wide range of applications of twistor theory.

An introduction to geometrical topics used in applied mathematics and theoretical physics.

A complete presentation of the theory of differential spaces, with applications to the study of singularities in systems with symmetry.

A complete presentation of the theory of differential spaces, with applications to the study of singularities in systems with symmetry.

This book, one of the first on G2 manifolds in decades, collects introductory lectures and survey articles largely based on talks given at a workshop held at the Fields Institute in August 2017, as part of the major thematic program on geometric analysis.

Fill in any gaps in your knowledge with this overview of key topics in undergraduate mathematics, now with four new chapters.

Fill in any gaps in your knowledge with this overview of key topics in undergraduate mathematics, now with four new chapters.

Geodesic and Horocyclic Trajectories presents an introduction to the topological dynamics of two classical flows associated with surfaces of curvature -1, namely the geodesic and horocycle flows.

This original monograph aims to explore the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces.

This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject.

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An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables.

The modern subject of differential forms subsumes classical vector calculus.

Differential geometry is the study of the curvature and calculus of curves and surfaces.

Reprinted as it originally appeared in the 1990s, this work is as an affordable text that will be of interest to a range of researchers in geometric analysis and mathematical physics.

Hans Duistermaat, an influential geometer-analyst, made substantial contributions to the theory of ordinary and partial differential equations, symplectic, differential, and algebraic geometry, minimal surfaces, semisimple Lie groups, mechanics, mathematical physics, and related fields.

One of the mathematical challenges of modern physics lies in the development of new tools to efficiently describe different branches of physics within one mathematical framework.

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 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.

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.