Differential and Riemannian geometry Books

The book presents in comprehensive detail numerical solutions to boundary value problems of a number of non-linear differential equations. Replacing derivatives by finite difference approximations in these differential equations leads to a system of...

This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf...

. E C, 0 < 1>'1 < 1, and n E Z, n ~ 2. Let~.>. be the O-dimensional Lie n group generated by the transformation z ~ >.z, z E C - {a}. Then (cf.

The papers in this volume are based on lectures given during the meeting of the Seminaire Sud Rhodanien de Geometrie which we organized at MSRI from May 22 to June 2, 1989, as part of a year-long program on Symplectic Geometry...

Starting at an introductory level, the book leads rapidly to important and often new results in synthetic differential geometry. From rudimentary analysis the book moves to such important results as: a new proof of De Rham's...

Harmonic maps are solutions to a natural geometrical variational prob­ lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also...

* Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. * Mean curvature flow and related...

 In 1993, M Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry. Mirror symmetry had been discovered by physicists in string theory as a duality between families of three-dimensional Calabi–Yau manifolds...

This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored,...

Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity.The first part is a concise and self-contained introduction to the basics of manifolds, differential forms,...

This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other...

This volume collects lecture notes from courses offered at several conferences and workshops, and provides the first exposition in book form of the basic theory of the Kähler-Ricci flow and its current state-of-the-art. While several excellent books on...

This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the...

This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gamma-convergence tools, applications of geometric measure theory, properties of interfacial...

This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing.  Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept...

This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen...

This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based...

This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics. Making intense use of the most advanced concepts from...

This concise, fast-paced text introduces the concepts and applications behind plane networks. It presents fundamental material from linear algebra and differential equations, and offers several different applications of the...

Original, well-written work of interestPresents for the first time (physical) field theories written in sheaf-theoretic languageContains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatmentsAuthor's...

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...

This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with...

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It...

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the...

The subject of space-filling curves has fascinated mathematicians for over a century and has intrigued many generations of students of mathematics. Working in this area is like skating on the edge of reason. Unfortunately, no...

Thomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. Here, he provides a clear and comprehensive modern treatment of the subject, as well as its applications to the study of Euclidean submanifolds...

The papers collected in this volume are contributions to the 43rd session of the Seminaire ´ de mathematiques ´ superieures ´ (SMS) on "Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology." This session took...

Most topics dealt with here deal with complex analysis of both one and several complex variables. Several contributions come from elasticity theory. Areas covered include the theory of p-adic analysis, mappings of bounded mean...

Dieses Buch enthält eine Einführung in die Differentialgeometrie, einer Teilgebiet der Mathematik, das sich mit der geometrischen Struktur von Räumen und Flächen im n-dimensionalen Raum befasst. Der Autor behandelt Themen wie Kurven, Krümmung, Flächen,...

Dans ce livre, Gaston Darboux présente une étude approfondie sur les surfaces mathématiques et leurs propriétés. Les lecteurs découvriront une analyse claire et précise de différents types de surfaces, ainsi que des problèmes liés à leur courbure et leur...

tEl moi, "0, si j'avait su comment en revenir, je One service mathematics has rendered the n 'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty...

One service mathematics has rendered the 'Et moi, ... , si j'avait su comment en revenir, je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty...

The problem of finding minimal surfaces, i. e. of finding the surface of least area among those bounded by a given curve, was one of the first considered after the foundation of the calculus of variations, and is one which...

This introductory text, based largely on examples and applications of general theory, covers commutative harmonic analysis, compact and finite groups, Lie groups, and the Heisenberg group and semidirect products. 1992 edition.

Introduction.- Part I Exterior and Differential Forms.- Exterior Forms and the Notion of Divisibility.- Differential Forms.- Dimension Reduction.- Part II Hodge-Morrey Decomposition and Poincaré Lemma.- An Identity Involving Exterior Derivatives and...

This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's...

This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and...

Driven by numerous examples from the complex geometric viewpoint New results presented for the first time Widely accessible, with all necessary background material provided for the nonspecialist Comparisons with classical...

Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis are employed in CR geometry Many examples and explicitly...

* Invited articles in differential geometry and mathematical physics in honor of Hideki Omori * Focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, Lie group theory,...

* Focuses on two fundamental questions related to semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications, and branching laws for unitary representations * Wide applications of...

Many mathematics books suffer from schizophrenia, and this is yet another. On the one hand it tries to be a reference for the basic results on flat riemannian manifolds. On the other hand it attempts to be a textbook which can...