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008 081109s2001 riua |b 001 0 eng
020 _a082182709X (alk. paper)
039 9 _a201402040056
_bVLOAD
_c201010020828
_dmalmash
_c200811101322
_dvenkatrajand
_c200811091256
_dNoora
_y200811091255
_zNoora
050 0 0 _aQA641
_b.A795 2001
100 1 _aAubin, Thierry.
_910388
245 1 2 _aA Course in Differential Geometry /
_cThierry Aubin.
260 _aProvidence, R.I. :
_bAmerican Mathematical Society,
_cc2001.
300 _axi, 184 p. :
_bill. ;
_c27 cm.
440 0 _aGraduate studies in mathematics,
_x1065-7339 ;
_vv. 27
_910389
504 _aIncludes bibliographical references (p. 177) and index.
505 _aBackground material Differentiable manifolds Tangent space Integration of vector fields and differential forms Linear connections Riemannian manifolds The Yamabe problem-An introduction to research Bibliography Subject index Notation.
520 _aThis textbook for second-year graduate students is intended as an introduction to differential geometry with principal emphasis on Riemannian geometry. Chapter I explains basic definitions and gives the proofs of the important theorems of Whitney and Sard. Chapter II deals with vector fields and differential forms. Chapter III addresses integration of vector fields and
_-plane fields. Chapter IV develops the notion of connection on a Riemannian manifold considered as a means to define parallel transport on the manifold.The author also discusses related notions of torsion and curvature, and gives a working knowledge of the covariant derivative. Chapter V specializes on Riemannian manifolds by deducing global properties from local properties of curvature, the final goal being to determine the manifold completely. Chapter VI explores some problems in PDEs suggested by the geometry of manifolds. The author is well known for his significant contributions to the field of geometry and PDEs - particularly for his work on the Yamabe problem - and for his expository accounts on the subject. The text contains many problems and solutions, permitting the reader to apply the theorems and to see concrete developments of the abstract theory.
650 0 _aGeometry, Differential.
_9904
942 _2lcc
_n0
_cBK
999 _c3695
_d3695