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Field name	Details
Dewey Class	516.373
Title	Riemannian Geometry ([EBook]) / by Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine.
Author	Gallot, Sylvestre. , 1948-
Added Personal Name	Hulin, Dominique
Added Personal Name	Lafontaine, Jacques
Other name(s)	SpringerLink (Online service)
Edition statement	Third Edition.
Publication	Berlin, Heidelberg : Springer , 2004.
Physical Details	XV, 322 pages, 58 illus. : online resource.
Series	Universitext 0172-5939
ISBN	9783642188558
Summary Note	Many years have passed since the ?rst edition. However, the encouragements of various readers and friends have persuaded us to write this third edition. During these years, Riemannian Geometry has undergone many dramatic - velopments. Here is not the place to relate them. The reader can consult for instance the recent book [Br5]. of our “mentor” Marcel Berger. However,R- mannian Geometry is not only a fascinating ?eld in itself. It has proved to be a precious tool in other parts of mathematics. In this respect, we can quote the major breakthroughs in four-dimensional topology which occurred in the eighties and the nineties of the last century (see for instance [L2]). These have been followed, quite recently, by a possibly successful approach to the Poincar´ e conjecture. In another direction, Geometric Group Theory, a very active ?eld nowadays (cf. [Gr6]), borrows many ideas from Riemannian or metric geometry. Butletusstophoggingthelimelight.Thisisjustatextbook.Wehopethatour point of view of working intrinsically with manifolds as early as possible, and testingeverynewnotiononaseriesofrecurrentexamples(seetheintroduction to the ?rst edition for a detailed description), can be useful both to beginners and to mathematicians from other ?elds, wanting to acquire some feeling for the subject.:
Contents note	1 Differential manifolds -- 1.A From submanifolds to abstract manifolds -- 1.B The tangent bundle -- 1.C Vector fields -- 1.D Baby Lie groups -- 1.E Covering maps and fibrations -- 1.F Tensors -- 1.G. Differential forms -- 1.H Partitions of unity -- 2 Riemannian metrics -- 2.A Existence theorems and first examples -- 2.B Covariant derivative -- 2.C Geodesies -- 2.D A glance at pseudo-Riemannian manifolds -- 3 Curvature -- 3.A. The curvature tensor -- 3.B. First and second variation -- 3.C. Jacobi vector fields -- 3.D. Riemannian submersions and curvature -- 3.E. The behavior of length and energy in the neighborhood of a geodesic -- 3.F Manifolds with constant sectional curvature -- 3.G Topology and curvature: two basic results -- 3.H. Curvature and volume -- 3.I. Curvature and growth of the fundamental group -- 3.J. Curvature and topology: some important results -- 3.K. Curvature tensors and representations of the orthogonal group -- 3.L. Hyperbolic geometry -- 3.M. Conformai geometry -- 4 Analysis on manifolds -- 4.A. Manifolds with boundary -- 4.B. Bishop inequality -- 4.C. Differential forms and cohomology -- 4.D. Basic spectral geometry -- 4.E. Some examples of spectra -- 4.F The minimax principle -- 4.G Eigenvalues estimates -- 4.H. Paul Levy’s isoperimetric inequality -- 5 Riemannian submanifolds -- 5.A. Curvature of submanifolds -- 5.B Curvature and convexity -- 5.C Minimal surfaces -- A Some extra problems -- B Solutions of exercises -- List of figures.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-642-18855-8
Links to Related Works	Subject References: Differential Geometry . Geometry, Riemannian . Mathematics . Authors: author . Gallot, Sylvestre. 1948- . Hulin, Dominique . Lafontaine, Jacques . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 516.373 . 516.373 (DDC 22) .

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Riemannian Geometry

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