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001 11319450
003 OSt
005 20160920171744.0
006 m d
007 cr n
008 121227s1987 gw | s |||| 0|eng d
020 _a9783540204930 (Pbk)
_cEuro 16.99
024 7 _a10.1007/978-3-642-97026-9
_2doi
035 _a(WaSeSS)ssj0001298324
040 _dWaSeSS
_cIISERB
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
082 0 4 _a516.36 G138R3
_223
100 1 _aGallot, Sylvestre.
_95537
210 1 0 _aRiemannian Geometry
222 _aMathematics Collection
245 1 0 _aRiemannian geometry:
_cby Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine.
250 _a3rd
260 _aHeidelberg:
_bSpringer,
_c2004.
300 _axv, 322p.
490 1 _aUniversitext,
_x0172-5939
505 0 _aI: Differential Manifolds -- A. from Submanifolds to Abstract Manifolds -- B. Tangent Bundle -- C. Vector Fields: -- D. Baby lie Groups -- E. Covering maps and Fibrations -- F. Tensors -- G. Exterior forms -- H. Appendix: Partitions of Unity -- II: Riemannian Metrics -- A. Existence Theorems and first Examples -- B. Covariant Derivative -- C. Geodesics -- III: Curvature -- A. the Curvature Tensor -- B. first Second Variation of arc-Length and Energy -- C. Jacobi Vector Fields -- D. Riemannian Submersions and Curvature -- E. The Behavior of Length and Energy in the Neighborhood of a Geodesic -- F. Manifolds with Constant Sectional Curvature -- G. Topology and Curvature -- H. Curvature and Volume -- I. Curvature and Growth of the Fundamental Group -- J. Curvature and Topology -- K. Curvature and Representations of the Orthogonal Group -- Chapitre IV: Analysis on Manifolds and the Ricci Curvature -- A. Manifolds with Boundary -- B. Bishop's Inequality Revisited -- C. Differential forms and Cohomology -- D. Basic Spectral Geometry -- E. Some Examples of Spectra -- F. The Minimax Principle -- V. Riemannian Submanifolds.
506 _aLicense restrictions may limit access.
520 _aTraditional point of view: pinched manifolds 147 Almost flat pinching 148 Coarse point of view: compactness theorems of Gromov and Cheeger 149 K. CURVATURE AND REPRESENTATIONS OF THE ORTHOGONAL GROUP Decomposition of the space of curvature tensors 150 Conformally flat manifolds 153 The second Bianchi identity 154 CHAPITRE IV : ANALYSIS ON MANIFOLDS AND THE RICCI CURVATURE A. MANIFOLDS WITH BOUNDARY Definition 155 The Stokes theorem and integration by parts 156 B. BISHOP'S INEQUALITY REVISITED 159 Some commutations formulas Laplacian of the distance function 160 Another proof of Bishop's inequality 161 The Heintze-Karcher inequality 162 C. DIFFERENTIAL FORMS AND COHOMOLOGY The de Rham complex 164 Differential operators and their formal adjoints 165 The Hodge-de Rham theorem 167 A second visit to the Bochner method 168 D. BASIC SPECTRAL GEOMETRY 170 The Laplace operator and the wave equation Statement of the basic results on the spectrum 172 E. SOME EXAMPLES OF SPECTRA 172 Introduction The spectrum of flat tori 174 175 Spectrum of (sn, can) F. THE MINIMAX PRINCIPLE 177 The basic statements VIII G. THE RICCI CURVATURE AND EIGENVALUES ESTIMATES Introduction 181 Bishop's inequality and coarse estimates 181 Some consequences of Bishop's theorem 182 Lower bounds for the first eigenvalue 184 CHAPTER V : RIEMANNIAN SUBMANIFOLDS A. CURVATURE OF SUBMANIFOLDS Introduction 185 Second fundamental form 185 Curvature of hypersurfaces 187 Application to explicit computations of curvature 189 B. CURVATURE AND CONVEXITY 192 The Hadamard theorem C.
650 0 _aMathematics.
_95538
650 0 _aGlobal differential geometry.
_95539
650 0 _aCell aggregation
_xMathematics.
_95540
650 0 _aMathematical physics.
_95541
650 1 4 _aMathematics.
_95538
650 2 4 _aDifferential Geometry.
_95542
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
_95543
650 2 4 _aMathematical Methods in Physics.
_95544
650 2 4 _aNumerical and Computational Physics.
_95545
700 1 _aHulin, Dominique.
_95546
700 1 _aLafontaine, Jacques.
_95547
773 0 _tSpringer eBooks
773 0 _tSpringerLink ebooks - Mathematics and Statistics (Archive)
776 0 8 _iPrinted edition:
_z9783540179238
830 0 _aUniversitext,
_95549
856 4 0 _zFull text available from SpringerLink ebooks - Mathematics and Statistics (Archive)
910 _aVendor-generated brief record
942 _2ddc
_cBK
999 _c6830
_d6830