LEADER 03753nam 22005655 450 001 9910300260503321 005 20250916144224.0 010 $a3-319-20735-0 024 7 $a10.1007/978-3-319-20735-3 035 $a(CKB)3710000000454155 035 $a(SSID)ssj0001558569 035 $a(PQKBManifestationID)16184054 035 $a(PQKBTitleCode)TC0001558569 035 $a(PQKBWorkID)14819507 035 $a(PQKB)11299705 035 $a(DE-He213)978-3-319-20735-3 035 $a(MiAaPQ)EBC6312520 035 $a(MiAaPQ)EBC5587007 035 $a(Au-PeEL)EBL5587007 035 $a(OCoLC)915767469 035 $a(PPN)187685649 035 $a(EXLCZ)993710000000454155 100 $a20150729d2015 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 13$aAn Introduction to Differential Manifolds /$fby Jacques Lafontaine 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XIX, 395 p. 49 illus.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-319-20734-2 320 $aIncludes bibliographical references and index. 327 $aDifferential Calculus -- Manifolds: The Basics -- From Local to Global -- Lie Groups -- Differential Forms -- Integration and Applications -- Cohomology and Degree Theory -- Euler-Poincaré and Gauss-Bonnet. 330 $aThis book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of ?abstract? notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory. The original French text Introduction aux variétés différentielles has been a best-seller in its category in France for many years. Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs. 606 $aGeometry, Differential 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 615 0$aGeometry, Differential. 615 14$aDifferential Geometry. 676 $a516.36 700 $aLafontaine$b Jacques$4aut$4http://id.loc.gov/vocabulary/relators/aut$056846 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300260503321 996 $aIntroduction aux variétés différentielles$92440566 997 $aUNINA