LEADER 03772nam 2200613 a 450 001 9910813583903321 005 20230721030803.0 010 $a1-281-91150-X 010 $a9786611911508 010 $a981-277-029-1 035 $a(CKB)1000000000403595 035 $a(OCoLC)646768317 035 $a(CaPaEBR)ebrary10255518 035 $a(SSID)ssj0000190884 035 $a(PQKBManifestationID)11177788 035 $a(PQKBTitleCode)TC0000190884 035 $a(PQKBWorkID)10183536 035 $a(PQKB)11402526 035 $a(MiAaPQ)EBC3050882 035 $a(WSP)00006528 035 $a(Au-PeEL)EBL3050882 035 $a(CaPaEBR)ebr10255518 035 $a(CaONFJC)MIL191150 035 $a(iGPub)WSPCB0002391 035 $a(EXLCZ)991000000000403595 100 $a20070618d2007 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on the geometry of manifolds /$fby Liviu I. Nicolaescu 205 $a2nd ed. 210 $aNew Jersey $cWorld Scientific$dc2007 215 $a1 online resource (606 p.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a981-277-862-4 311 $a981-270-853-7 320 $aIncludes bibliographical references (p. 579-582) and index. 327 $a1. Introduction -- 2. Natural constructions on manifolds -- 3. Calculus on manifolds -- 4. Riemannian geometry -- 5. Elements of the calculus of variations -- 6. The fundamental group and covering spaces -- 7. Cohomology -- 8. Characteristic classes -- 9. Classical integral geometry -- 10. Elliptic equations on manifolds -- 11. Dirac operators. 330 $a"The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology. The book's guiding philosophy is, in the words of Newton, that ?in learning the sciences examples are of more use than precepts?. We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue. While we present most of the local aspects of classical differential geometry, the book has a ?global and analytical bias?. We develop many algebraic-topological techniques in the special context of smooth manifolds such as Poincaré duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss?Bonnet theorem. We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lpand Hölder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators. The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight." 606 $aGeometry, Differential 606 $aManifolds (Mathematics) 615 0$aGeometry, Differential. 615 0$aManifolds (Mathematics) 676 $a516.3/62 700 $aNicolaescu$b Liviu I$067532 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910813583903321 996 $aLectures on the geometry of manifolds$9899816 997 $aUNINA