000 02171nam a22001817a 4500
008 220809b2021 |||||||| |||| 00| 0 eng d
020 _a9780000990334
082 _a516.362 NIC-L
100 _aNicolaescu, Liviu I
245 _aLectures on the geometry of manifolds /
_cLiviu I Nicolaescu
250 _a3rd ed.
260 _aSingapore
_bWorld Scientific
_c2021
300 _a682 p.
365 _aINR
_b1995.00.
500 _aThe 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.
650 _aGeometry, Differential
650 _aManifolds (Mathematics)
999 _c79890
_d79890