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Curvature in Mathematics and Physics

Curvature in Mathematics and Physics

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作者: Shlomo Sternberg 著

出版社: Dover Publications

出版时间: 2012-09

版次: 1

ISBN: 9780486478555

定价: 170.40

装帧: 平装

开本: 其他

纸张: 其他

页数: 416页

正文语种: 英语

丛书: Dover Books on Mathematics

分类: 外文古旧书>英文书>工程技术

Thisoriginaltextforcoursesindifferentialgeometryisgearedtowardadvancedundergraduateandgraduatemajorsinmathandphysics.Basedonanadvancedclasstaughtbyaworld-renownedmathematicianformorethanfiftyyears,thetreatmentintroducessemi-Riemanniangeometryanditsprincipalphysicalapplication,Einstein'stheoryofgeneralrelativity,usingtheCartanexteriorcalculusasaprincipaltool.
StartingwithanintroductiontothevariouscurvaturesassociatedtoahypersurfaceembeddedinEuclideanspace,thetextadvancestoabriefreviewofthedifferentialandintegralcalculusonmanifolds.Adiscussionofthefundamentalnotionsoflinearconnectionsandtheircurvaturesfollows,alongwithconsiderationsofLevi-Civita'stheorem,bi-invariantmetricsonaLiegroup,Cartancalculations,Gauss'slemma,andvariationalformulas.AdditionaltopicsincludetheHopf-Rinow,Myer's,andFrobeniustheorems;specialandgeneralrelativity;connectionsonprincipalandassociatedbundles;thestaroperator;superconnections;semi-Riemanniansubmersions;andPetrovtypes.Prerequisitesincludelinearalgebraandadvancedcalculus,preferablyinthelanguageofdifferentialforms.
内容简介:
Thisoriginaltextforcoursesindifferentialgeometryisgearedtowardadvancedundergraduateandgraduatemajorsinmathandphysics.Basedonanadvancedclasstaughtbyaworld-renownedmathematicianformorethanfiftyyears,thetreatmentintroducessemi-Riemanniangeometryanditsprincipalphysicalapplication,Einstein'stheoryofgeneralrelativity,usingtheCartanexteriorcalculusasaprincipaltool.
StartingwithanintroductiontothevariouscurvaturesassociatedtoahypersurfaceembeddedinEuclideanspace,thetextadvancestoabriefreviewofthedifferentialandintegralcalculusonmanifolds.Adiscussionofthefundamentalnotionsoflinearconnectionsandtheircurvaturesfollows,alongwithconsiderationsofLevi-Civita'stheorem,bi-invariantmetricsonaLiegroup,Cartancalculations,Gauss'slemma,andvariationalformulas.AdditionaltopicsincludetheHopf-Rinow,Myer's,andFrobeniustheorems;specialandgeneralrelativity;connectionsonprincipalandassociatedbundles;thestaroperator;superconnections;semi-Riemanniansubmersions;andPetrovtypes.Prerequisitesincludelinearalgebraandadvancedcalculus,preferablyinthelanguageofdifferentialforms.

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