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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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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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Analysis on Manifolds

Analysis on Manifolds more books like this

by James R Munkres

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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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Relativity on Curved Manifolds

Relativity on Curved Manifolds more books like this

by F De Felice, C J S Clarke

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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Applied Exterior Calculus

Applied Exterior Calculus more books like this

by Dominic 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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Manifolds, Tensor Analysis, and Applications

Manifolds, Tensor Analysis, and Applications more books like this

by Ralph Abraham, Jerrold E Marsden, Tudor Stefan Ratiu

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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Statistics on Special Manifolds

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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Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations

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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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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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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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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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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Initiation to Global Finslerian Geometry more books like this

by H Akbar-Zadeh

After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next ...

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

by Robion C Kirby

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Metric Diophantine Approximation on Manifolds more books like this

by V I Bernik, M M Dodson, Bela Bollobas (Editor)

This book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space, and its aim is to develop a coherent body of theory comparable with that which already exists for classical Diophantine approximation. In particular, this book deals with Khintchine-type theorems and with the Hausdorff dimension of the associated ...

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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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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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Compact Manifolds with Special Holonomy more books like this

by Dominic D Joyce

The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Kahler geometry. Then the Calabi conjecture is proved and used to deduce the existence of compact manifolds with holonomy SU(m) (Calabi-Yau manifolds) and Sp(m) (hyperkahler manifolds). These are constructed and studied using complex ...

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Crack Theory and Edge Singularities more books like this

by David Kapanadze, B Wolfgang Schulze

The book studies boundary value problems connected with geometric singularities and models of the crack theory. New and interesting phenomena on the behaviour of solutions (regularity in weighted spaces, asymptotics) are analysed by means of parametrices obtained by inverting corresponding scalar and operator-valued symbols. Compared with other ...

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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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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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Generalized Manifolds more books like this

by Karl-Georg Schlesinger, K-G Schlesinger

In this Research Note, a generalization of the subject of differential geometry is developed, using techniques and results of nonstandard analysis. This generalization is found to correspond to approximations of classical manifolds by set-theoretic near manifold structures. Schlesinger develops several applications of the theory in the fields of ...

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Smoothings of Piecewise Linear Manifolds more books like this

by Morris W Hirsch, Barry Mazur

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