Download Lectures on Fibre Bundles and Differential Geometry by J. L. Koszul (auth.) PDF

By J. L. Koszul (auth.)

ISBN-10: 354012876X

ISBN-13: 9783540128762

ISBN-10: 3662025035

ISBN-13: 9783662025031

I Differential calculus.- II Differentiable bundles.- III Connections on crucial bundles.- IV Holonomy groups.- V Vector bundles and derivation laws.- VI Holomorphic connections.- References.

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Download Differentialgeometrie und Minimalflächen by Jürgen Jost (auth.) PDF

By Jürgen Jost (auth.)

ISBN-10: 3540569049

ISBN-13: 9783540569046

ISBN-10: 3662067188

ISBN-13: 9783662067185

Das vorliegende Lehrbuch bietet eine moderne Einf?hrung in die Differentialgeometrie etwa im Umfang einer einsemestrigen Vorlesung. Zun?chst wird die Geometrie von Fl?chen im Raum behandelt. Hierbei wird die geometrische Anschauung des Lesers anhand vieler Beispiele gef?rdert, deren wichtigste Klasse die Minimalfl?chen bilden. Zu ihrem Studium werden analytische Methoden entwickelt, und in diesem Zusammenhang wird auch das Plateausche challenge, eine Minimalfl?che mit vorgegebener Berandung zu finden, gel?st. Als Beispiel einer globalen Aussage der Differentialgeometrie wird der Bernsteinsche Satz bewiesen. Weitere Kapitel behandeln die innere Geometrie von Fl?chen, einschlie?lich des Satzes von Gauss-Bonnet und einer ausf?hrlichen Darstellung der hyperbolischen Geometrie. Verschiedene geistesgeschichtliche Bemerkungen runden diesen textual content ab, welcher durch seine Verbindung von geometrischen Konstruktionen und analytischen Methoden einem zentralen pattern der modernen mathematischen Forschung folgt. Das erste Lehrbuch, das eine gr?ndliche Einf?hrung in die Theorie der Minimalfl?chen gew?hrleistet.

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Download Einstein Manifolds (Classics in Mathematics) by Arthur L. Besse PDF

By Arthur L. Besse

ISBN-10: 3540741208

ISBN-13: 9783540741206

Einstein's equations stem from common Relativity. within the context of Riemannian manifolds, an self sufficient mathematical idea has constructed round them. this is often the 1st booklet which offers an summary of a number of notable effects resulting from the exam of Einstein’s equations within the context of Riemannian manifolds. components of the textual content can be utilized as an creation to trendy Riemannian geometry via issues like homogeneous areas, submersions, or Riemannian functionals.

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Download Harmonic morphisms between Riemannian manifolds by Paul Baird, John C. Wood PDF

By Paul Baird, John C. Wood

ISBN-10: 0198503628

ISBN-13: 9780198503620

This is often the 1st account in ebook kind of the idea of harmonic morphisms among Riemannian manifolds. Harmonic morphisms are maps which defend Laplace's equation. they are often characterised as harmonic maps which fulfill an extra first order situation. Examples comprise harmonic services, conformal mappings within the airplane, and holomorphic capabilities with values in a Riemann floor. There are connections with many conepts in differential geometry, for instance, Killing fields, geodesics, foliations, Clifford platforms, twistor areas, Hermitian buildings, iso-parametric mappings, and Einstein metrics and likewise the Brownain pathpreserving maps of chance thought. Giving a whole account of the elemental facets of the topic, this ebook is self-contained, assuming just a uncomplicated wisdom of differential geometry.

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Download Symplectic actions of 2-tori on 4-manifolds by Alvaro Pelayo PDF

By Alvaro Pelayo

ISBN-10: 0821847139

ISBN-13: 9780821847138

During this paper the writer classifies symplectic activities of $2$-tori on compact hooked up symplectic $4$-manifolds, as much as equivariant symplectomorphisms. This extends result of Atiyah, Guillemin-Sternberg, Delzant and Benoist. The class is by way of a set of invariants of the topology of the manifold, of the torus motion and of the symplectic shape. the writer constructs particular types of such symplectic manifolds with torus activities, outlined by way of those invariants

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Download Riemannsche Geometrie im Großen by Detlef Gromoll, Visit Amazon's Wilhelm Klingenberg Page, PDF

By Detlef Gromoll, Visit Amazon's Wilhelm Klingenberg Page, search results, Learn about Author Central, Wilhelm Klingenberg, , Wolfgang Meyer

ISBN-10: 3540071334

ISBN-13: 9783540071334

Aus dem Vorwort: "Globale Probleme der Differentialgeometrie erfreuen sich eines immer noch wachsenden Interesses. Gerade in der Riemannschen Geometrie hat die Frage nach Beziehungen zwischen Riemannscher und topologischer Struktur in neuerer Zeit zu vielen sch?nen und ?berraschenden Einsichten gef?hrt. Dabei denken wir hier vor allem an den Problemkreis: Welche topologischen Invarianten werden charakterisiert durch eine der wichtigsten isometrischen Invarianten, die Kr?mmung? Ziel der folgenden Noten ist, einige zentrale Resultate in dieser Richtung darzustellen.... Wir haben uns bem?ht, die Darstellung m?glichst elementar und in sich abgeschlossen zu halten und einen einfachen leistungsf?higen Kalk?l zu entwickeln."

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Download Tensor Algebra and Tensor Analysis for Engineers: With by Mikhail Itskov PDF

By Mikhail Itskov

ISBN-10: 3540939067

ISBN-13: 9783540939061

ISBN-10: 3540939075

ISBN-13: 9783540939078

There's a huge hole among engineering classes in tensor algebra on one hand, and the remedy of linear adjustments inside of classical linear algebra at the different. This ebook addresses essentially engineering scholars with a few preliminary wisdom of matrix algebra. Thereby, mathematical formalism is utilized so far as it truly is completely important. various workouts supplied within the e-book are followed through suggestions permitting self reliant examine. The final chapters care for sleek advancements within the concept of isotropic and anisotropic tensor services and their functions to continuum mechanics and can for that reason be of excessive curiosity for PhD-students and scientists operating during this sector.

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Download Geometric Curve Evolution and Image Processing by Frédéric Cao PDF

By Frédéric Cao

ISBN-10: 0195169719

ISBN-13: 9780195169713

In picture processing, "motions via curvature" offer a good strategy to delicate curves representing the bounds of items. In this type of movement, every one aspect of the curve strikes, at any quick, with a regular speed equivalent to a functionality of the curvature at this element. This ebook is a rigorous and self-contained exposition of the concepts of "motion by means of curvature". The technique is axiomatic and formulated when it comes to geometric invariance with admire to the placement of the observer. this can be translated into mathematical phrases, and the writer develops the method of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then attracts a whole parallel with one other axiomatic procedure utilizing level-set tools: this results in generalized curvature motions. eventually, novel, and extremely exact, numerical schemes are proposed permitting one to compute the answer of hugely degenerate evolution equations in a totally invariant method. The convergence of this scheme can be proved.

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