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Tensor analysis on manifolds

Tensor analysis on manifolds more books like this

by Richard L. Bishop

Proceeds from general to special, including chapters on vector analysis on manifolds and integration theory.

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Analysis on Manifolds

Analysis on Manifolds more books like this

by James R Munkres

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Introduction to Manifolds

Introduction to Manifolds more books like this

by Loring W Tu

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds ...

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Flow Lines and Algebraic Invariants in Contact Form Geometry

Flow Lines and Algebraic Invariants in Contact Form Geometry more books like this

by Abbas Bahri

This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology). In particular, this work develops a novel algebraic tool in this field: rooted in the concept of critical ...

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Invariant Manifolds and Fibrations for Perturbed Nonlinear Schradinger Equations

Invariant Manifolds and Fibrations for Perturbed Nonlinear Schradinger Equations more books like this

by Charles Li, Stephen Wiggins, David McLaughlin

The nonlinear Schroedinger (NLS) equation is a fundamental nonlinear partial differential equation (PDE) that arises in many areas and engineering, e.g. in plasma physics, nonlinear waves, and nonlinear optics. It is an example of a completely integrable PDE where phase space structure is known in some detail. In this monograph the authors present ...

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Introduction to Smooth Manifolds

Introduction to Smooth Manifolds more books like this

by John M Lee

This book is an introductory graduate-level textbook on the theory of smooth manifolds, for students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis. It is a natural sequel to the author's last book, Introduction to Topological ...

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Lectures on the Geometry of Manifolds

Lectures on the Geometry of Manifolds more books like this

by Liviu I Nicolaescu

The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology. The book's ...

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Relativity on Curved Manifolds

Relativity on Curved Manifolds more books like this

by De Felice, Clarke 1946-

This is a self-contained exposition of general relativity with emphasis given to tetrad and spinor structures and physical measurements on curved manifolds. General relativity is now essential to the understanding of modern physics, but the power of the theory cannot be fully explained without a detailed knowledge of its mathematical structure. ...

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Hypo-Analytic Structures: Local Theory

Hypo-Analytic Structures: Local Theory more books like this

by Francois Treves

In "Hypo-Analytic Structures" Francois Treves provides a systematic approach to the study of the differential structures on manifolds defined by systems of complex vector fields. Serving as his main examples are the elliptic complexes, among which the De Rham and Dolbeault are the best known and the tangential Cauchy-Riemann operators. Basic ...

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Smooth Manifolds and Observables

Smooth Manifolds and Observables more books like this

by Jet Nestruev

This book is a self-contained introduction to fiber spaces and differential operators on smooth manifolds that is accessible to graduate students specializing in mathematics and physics. Over the last 20 years the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be ...

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Manifolds, Tensor Analysis, and Applications more books like this

by Ralph Abraham, Jerrold E. Marsden

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid mechanics, electromagnetism, plasma ...

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Manifolds with singularities and the Adams-Novikov spectral sequence more books like this

by Botvinnik

Traditionally the Adams-Novikov spectral sequence has been a tool which has enabled the computation of generators and relations to describe homotopy groups. Here a natural geometric description of the sequence is given in terms of cobordism theory and manifolds with singularities. The author brings together many interesting results not widely ...

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Applied Exterior Calculus more books like this

by Dominic G B Edelen

This book gives an applied introduction to exterior calculus for upper division undergraduates and beginning graduate students. Development is operational with an emphasis on computation proficiency and elementary geometric notions. Consideration is limited to local questions. The book also features fully worked out examples and problems with ...

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A course in mathematical physics more books like this

by Walter E Thirring

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Algebraic and Geometric Topology more books like this

by James R Milgram (Editor)

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Complex, Contact and Symmetric Manifolds: In Honor of L. Vanhecke more books like this

by Oldrich Kowalski (Editor), Emilio Musso (Editor), Domenico Perrone (Editor)

This volume contains research and survey articles by well known and respected mathematicians on 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. The papers, all written with the necessary introductory and contextual ...

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Foundational Essays on Topological Manifolds, Smoothings, and Triangulations more books like this

by Robion C Kirby

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An Introduction to Dirac Operators on Manifolds more books like this

by Jan Cnops

Dirac operators play an important part in several domains of mathematics and mathematical physics, for example: index theory, theory of elliptic pseudodifferential operators, theory of electromagnetism, particle physics, and representation theory of Lie groups. In this work, the basic theories underlying the concept of Dirac operators are explored ...

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Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations more books like this

by P Constantin, C Foias, B Nicolaenko

This work, the main results of which were announced in (CFNT), focuses on a new geometric explicit construction of inertial manifolds from integral manifolds generated by some initial dimensional surface. The method covers a large class of dissipative PDEs. The existence of a smooth integral manifold the closure of which in an inertial manifold M ...

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Integration on Infinite-Dimensional Surfaces and Its Applications more books like this

by A V Uglanov

This text presents the theory of integration over surfaces in abstract topological vector space. Applications of the theory in different fields, such as infinite dimensional distributions and differential equations (including boundary value problems), stochastic processes, approximation of functions, and calculus of variation on a Banach space, ...

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Classifying Spaces for Surgery and Corbordism of Manifolds. (Am-92) more books like this

by IB Madsen, R James Milgram

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Geometry of Low-Dimensional Manifolds: Volume 1 more books like this

by S K Donaldson, C B Thomas (Editor)

This volume is based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research during the 1990s, with major breakthroughs that have illuminated the way a number of different subjects interact (for example: topology, differential and algebraic geometry ...

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Smooth Invariant Manifolds and Normal Forms more books like this

by I. U. Bronshtein

This volume deals with the qualitative theory of dynamical systems and is devoted to the study of flows and cascades in the vicinity of a smooth invariant manifold. Its main purpose is to present, as completely as possible, the basic results concerning the existence of stable and unstable local manifolds and the recent advancements in the theory ...

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Statistics on Special Manifolds more books like this

by Yasuko Chikuse

This book is concerned with statistical analysis on the two special manifolds, the Stiefel manifold and the Grassmann manifold, treated as statistical sample spaces consisting of matrices. The former is represented by the set of m x k matrices whose columns are mutually orthogonal k-variate vectors of unit length, and the latter by the set of m x ...

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Decompositions of Manifolds more books like this

by Robert J Daverman

Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and ...

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