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Differential Geometry

Download Applied Differential Geometry by William L. Burke PDF

By William L. Burke

This can be a self-contained introductory textbook at the calculus of differential types and smooth differential geometry. The meant viewers is physicists, so the writer emphasises functions and geometrical reasoning on the way to supply effects and ideas an exact yet intuitive which means with out getting slowed down in research. the big variety of diagrams is helping elucidate the elemental rules. Mathematical issues coated comprise differentiable manifolds, differential types and twisted varieties, the Hodge megastar operator, external differential platforms and symplectic geometry. the entire arithmetic is stimulated and illustrated by means of beneficial actual examples.

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Download Hamiltonian Mechanical Systems and Geometric Quantization by Mircea Puta PDF

By Mircea Puta

This quantity provides numerous facets of the geometry of symplectic and Poisson manifolds, and purposes in Hamiltonian mechanics and geometric quantization are indicated.
bankruptcy 1 provides a few basic proof approximately symplectic vector house, symplectic manifolds and symplectic relief. bankruptcy 2 offers with the research of Hamiltonian mechanics. bankruptcy three considers a few general evidence touching on Lie teams and algebras which result in the speculation of momentum mappings and the Marsden--Weinstein relief. Chapters four and five think about the idea and the soundness of equilibrium recommendations of Hamilton--Poisson mechanical structures. Chapters 6 and seven are dedicated to the idea of geometric quantization. This leads, in bankruptcy eight, to subject matters resembling foliated cohomology, the idea of the Dolbeault--Kostant complicated, and their purposes. A dialogue of the relation among geometric quantization and the Marsden--Weinstein aid is gifted in bankruptcy nine. the ultimate bankruptcy considers extending the speculation of geometric quantization to Poisson manifolds, through the speculation of symplectic groupoids.
every one bankruptcy concludes with difficulties and recommendations, a lot of which current major purposes and, at times, significant theorems.
For graduate scholars and researchers whose pursuits and paintings contain symplectic geometry and Hamiltonian mechanics.

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Download Introduction to the $h$-Principle by Y. Eliashberg PDF

By Y. Eliashberg

Eliashberg and Mishachev (credentials now not indexed) speak about equipment for proving the h-principle: holonomic approximation and convex integration. purposes to symplectic and make contact with geometry are emphasised. a quick textual content, the e-book is suited to a graduate-level path on geometric tools for fixing partial differential equations and inequalities. quite a few diagrams illustrate the foundations and ideas defined within the textual content.

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Download Harmonic Maps and Differential Geometry: A Harmonic Map Fest by E. Loubeau, S. Montaldo PDF

By E. Loubeau, S. Montaldo

This quantity includes the complaints of a convention held in Cagliari, Italy, from September 7-10, 2009, to have a good time John C. Wood's sixtieth birthday. those papers replicate the numerous elements of the idea of harmonic maps and its hyperlinks and connections with different subject matters in Differential and Riemannian Geometry. lengthy studies, one on consistent suggest curvature surfaces via F. Pedit and the opposite at the development of harmonic maps through J. C. wooden, open the lawsuits. those are via a mixture of surveys on Prof. Wood's strong point: Lagrangian surfaces, biharmonic maps, in the neighborhood conformally Kahler manifolds and the DDVV conjecture, in addition to numerous learn papers on harmonic maps. different learn papers within the quantity are dedicated to Willmore surfaces, Goldstein-Pedrich flows, touch pairs, prescribed Ricci curvature, conformal fibrations, the Fadeev-Hopf version, the Compact aid precept and the curvature of surfaces

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Download Differential Geometry: Basic Notions and Physical Examples by Marcelo Epstein PDF

By Marcelo Epstein

Differential Geometry bargains a concise advent to a couple uncomplicated notions of recent differential geometry and their functions to stable mechanics and physics.

Concepts similar to manifolds, teams, fibre bundles and groupoids are first brought inside of a simply topological framework. they're proven to be proper to the outline of space-time, configuration areas of mechanical platforms, symmetries quite often, microstructure and native and far-off symmetries of the constitutive reaction of continuing media.

Once those rules were grasped on the topological point, the differential constitution wanted for the outline of actual fields is brought when it comes to differentiable manifolds and important body bundles. those mathematical techniques are then illustrated with examples from continuum kinematics, Lagrangian and Hamiltonian mechanics, Cauchy fluxes and dislocation theory.

This ebook can be worthy for researchers and graduate scholars in technological know-how and engineering.

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