Category: Differential Geometry

Download Differential Geometry of Varieties with Degenerate Gauss by Maks A. Akivis, Vladislav V. Goldberg PDF

By Maks A. Akivis, Vladislav V. Goldberg

During this e-book the authors learn the differential geometry of types with degenerate Gauss maps. They use the most tools of differential geometry, specifically, the tools of relocating frames and external differential kinds in addition to tensor equipment. by way of those equipment, the authors detect the constitution of sorts with degenerate Gauss maps, ensure the singular issues and singular forms, locate focal photos and build a class of the kinds with degenerate Gauss maps.

The authors introduce the above pointed out equipment and observe them to a sequence of concrete difficulties bobbing up within the thought of types with degenerate Gauss maps. What makes this e-book detailed is the authors' use of a scientific software of equipment of projective differential geometry in addition to equipment of the classical algebraic geometry for learning forms with degenerate Gauss maps.

This booklet is meant for researchers and graduate scholars attracted to projective differential geometry and algebraic geometry and their purposes. it may be used as a textual content for complex undergraduate and graduate scholars.

Both authors have released over a hundred papers every one. each one has written a few books, together with Conformal Differential Geometry and Its Generalizations (Wiley 1996), Projective Differential Geometry of Submanifolds (North-Holland 1993), and Introductory Linear Algebra (Prentice-Hall 1972), which have been written by way of them together.

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Download Gradient flows: In metric spaces and in the space of by Luigi Ambrosio PDF

By Luigi Ambrosio

This booklet is dedicated to a concept of gradient flows in areas which aren't inevitably endowed with a ordinary linear or differentiable constitution. It involves components, the 1st one referring to gradient flows in metric areas and the second dedicated to gradient flows within the area of chance measures on a separable Hilbert house, endowed with the Kantorovich-Rubinstein-Wasserstein distance.

The components have a few connections, considering the distance of chance measures offers a huge version to which the "metric" thought applies, however the publication is conceived in this kind of method that the 2 elements may be learn independently, the 1st one through the reader extra attracted to non-smooth research and research in metric areas, and the second via the reader extra oriented in the direction of the purposes in partial differential equations, degree concept and probability.

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Download Morse Homology by Matthias Schwarz PDF

By Matthias Schwarz

This booklet provides a hyperlink among sleek research and topology. dependent upon classical Morse thought it develops the finite dimensional analogue of Floer homology which, within the contemporary years, has come to play an important function in geometry. Morse homology evidently arises from the gradient dynamical approach linked to a Morse functionality. The underlying chain advanced, already thought of via Thom, Smale, Milnor and Witten, analogously varieties the elemental aspect of Floer's homology concept. this idea of relative Morse conception together with Conley's continuation precept lends itself to an axiomatic homology functor. the current process consistenly employs analytic equipment in strict analogy with the development of Floers homology teams. that may be a calculus for yes nonlinear Fredholm operators on Banach manifolds which listed here are curve areas and in which the answer units shape the focal moduli areas. The publication bargains a scientific and complete presentation of the research of those moduli areas. All theorems inside this analytic time table comprising Fredholm concept, regularity and compactness effects, gluing and orientation research, including their proofs and pre-requisite fabric, are tested right here intimately. This exposition hence brings a methodological perception into present-day research.

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Download Anschauliche Geometrie by David Hilbert, Stephan Cohn-Vossen PDF

By David Hilbert, Stephan Cohn-Vossen

Anschauliche Geometrie: wohl selten ist ein Mathematikbuch seinem Titel so gerecht geworden, wie dieses außergewöhnliche Werk von Hilbert und Cohn-Vossen. Zuerst 1932 erschienen, hat das Buch nichts von seiner Frische und Kraft verloren. Hilbert hat sein erklärtes Ziel, die Faszination der Geometrie zu vermitteln, bei Generationen von Mathematikern erreicht.
AUS HILBERTS VORWORT: "Das Buch soll dazu dienen, die Freude an der Mathematik zu mehren, indem es dem Leser erleichtert, in das Wesen der Mathematik einzudringen, ohne sich einem beschwerlichen Studium zu unterziehen".

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Download Differential Geometry and Mathematical Physics by John K. Beem PDF

By John K. Beem

This booklet comprises the court cases of the specified consultation, Geometric tools in Mathematical Physics, held on the joint AMS-CMS assembly in Vancouver in August 1993. The papers gathered the following comprise a few new ends up in differential geometry and its purposes to physics. the main topics contain black holes, singularities, censorship, the Einstein box equations, geodesics, index thought, submanifolds, CR-structures, and space-time symmetries. furthermore, there are papers on Yang-Mills fields, geometric innovations on top of things idea, and equilibria. Containing new effects through verified researchers within the box, this booklet presents a glance at advancements during this intriguing quarter of analysis

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Download Differential Geometry (Wiley Classics Library) by J. J. Stoker PDF

By J. J. Stoker

This vintage paintings is now on hand in an unabridged paperback version. Stoker makes this fertile department of arithmetic obtainable to the nonspecialist by means of 3 varied notations: vector algebra and calculus, tensor calculus, and the notation devised by means of Cartan, which employs invariant differential types as parts in an algebra as a result of Grassman, mixed with an operation referred to as external differentiation. Assumed are a passing acquaintance with linear algebra and the fundamental components of research.

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Download A survey on classical minimal surface theory by William H., III Meeks, Joaquin Perez PDF

By William H., III Meeks, Joaquin Perez

Meeks and Pérez current a survey of contemporary outstanding successes in classical minimum floor idea. The class of minimum planar domain names in 3-dimensional Euclidean area offers the focal point of the account. The evidence of the class relies on the paintings of many presently lively top mathematicians, therefore making touch with a lot of an important leads to the sphere. during the telling of the tale of the type of minimum planar domain names, the overall mathematician may possibly trap a glimpse of the intrinsic great thing about this thought and the authors' point of view of what's occurring at this historic second in a truly classical topic. This booklet comprises an up-to-date travel via the various fresh advances within the conception, comparable to Colding-Minicozzi thought, minimum laminations, the ordering theorem for the distance of ends, conformal constitution of minimum surfaces, minimum annular ends with limitless overall curvature, the embedded Calabi-Yau challenge, neighborhood images at the scale of curvature and topology, the neighborhood detachable singularity theorem, embedded minimum surfaces of finite genus, topological category of minimum surfaces, forte of Scherk singly periodic minimum surfaces, and notable difficulties and conjectures

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Download Geometry IV: nonregular Riemannian geometry by Yu.G. Reshetnyak, E. Primrose, V.N. Berestovskij, I.G. PDF

By Yu.G. Reshetnyak, E. Primrose, V.N. Berestovskij, I.G. Nikolaev

This booklet includes surveys on sleek examine into non-regular Riemannian geometry, performed quite often by way of Russian mathematicians. insurance examines two-dimensional Riemannian manifolds of bounded curvature and metric areas whose curvature lies among given constants. This booklet might be immensely precious to graduate scholars and researchers in geometry, specifically Riemannian geometry.

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Download Differential geometry of complex vector bundles by Shoshichi Kobayashi PDF

By Shoshichi Kobayashi

Holomorphic vector bundles became gadgets of curiosity not just to algebraic and differential geometers and intricate analysts but in addition to low dimensional topologists and mathematical physicists engaged on gauge thought. This booklet, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate scholars in those a number of fields of mathematics.

Originally released in 1987.

The Princeton Legacy Library makes use of the newest print-on-demand know-how to back make to be had formerly out-of-print books from the celebrated backlist of Princeton college Press. those variants safeguard the unique texts of those very important books whereas featuring them in sturdy paperback and hardcover versions. The target of the Princeton Legacy Library is to greatly bring up entry to the wealthy scholarly background present in the hundreds of thousands of books released by way of Princeton collage Press considering the fact that its founding in 1905.

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