natural operations in differential geometry - ivan ,peter, jan

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1、NATURALOPERATIONSINDIFFERENTIALGEOMETRYIvanKolarPeterW.MichorJanSlovakMailingaddress:PeterW.Michor,Institutf•urMathematikderUniversit•atWien,Strudlhofgasse4,A-1090Wien,Austria.IvanKolar,JanSlovak,DepartmentofAlgebraandGeometryFacultyofScience,MasarykUniversityJanackovo

2、nam2a,CS-66295Brno,CzechoslovakiaElectronicedition.OriginallypublishedbySpringer-Verlag,BerlinHeidelberg1993,ISBN3-540-56235-4,ISBN0-387-56235-4.TypesetbyAMS-TEXvTABLEOFCONTENTSPREFACE............................1CHAPTERI.MANIFOLDSANDLIEGROUPS................41.Dierentiablem

3、anifolds.....................42.Submersionsandimmersions..................113.Vectoreldsand ows.....................164.Liegroups..........................305.Liesubgroupsandhomogeneousspaces.............41CHAPTERII.DIFFERENTIALFORMS...................496.Vectorbundles.......

4、.................497.Dierentialforms.......................618.DerivationsonthealgebraofdierentialformsandtheFr•olicher-Nijenhuisbracket...............67CHAPTERIII.BUNDLESANDCONNECTIONS...............769.Generalberbundlesandconnections..............7610.Principalberbundles

5、andG-bundles..............8611.Principalandinducedconnections...............99CHAPTERIV.JETSANDNATURALBUNDLES...............11612.Jets.............................11713.Jetgroups..........................12814.Naturalbundlesandoperators.................13815.Prolongationsofpri

6、ncipalberbundles.............14916.Canonicaldierentialforms..................15417.Connectionsandtheabsolutedierentiation...........158CHAPTERV.FINITEORDERTHEOREMS.................16818.Bundlefunctorsandnaturaloperators..............16919.Peetre-liketheorems................

7、......17620.Theregularityofbundlefunctors................18521.Actionsofjetgroups......................19222.Theorderofbundlefunctors..................20223.Theorderofnaturaloperators.................205CHAPTERVI.METHODSFORFINDINGNATURALOPERATORS......21224.PolynomialGL(V)-equ

8、ivariantmaps..............21325.Naturaloperatorsonlinearconne