Curvature in Mathematics and Physics

Curvature in Mathematics and Physics
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作者:
出版社: Dover Publications
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
  • 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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