UID:
almafu_9958104457802883
Umfang:
1 online resource (335 p.)
ISBN:
1-281-76631-3
,
9786611766313
,
0-08-087323-5
Serie:
Pure and applied mathematics ; 11
Inhalt:
Curvature and homology
Anmerkung:
Reprint. Originally published: New York : Academic Press, 1962 (1970 printing) (Pure and applied mathematics ; 11).
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Front Cover; Curvature and Homology; Copyright Page; Contents; Preface; Notation Index; Introduction; CHAPTER I. RIEMANNIAN MANIFOLDS; 1.1 Differentiable manifolds; 1.2 Tensors; 1.3 Tensor bundles; 1.4 Differential forms; 1.5 Submanifolds; 1.6 Integration of differential forms; 1.7 Affine connections; 1.8 Bundle of frames; 1.9 Riemannian geometry; 1.10 Sectional curvature; 1.11 Geodesic coordinates; Exercises; CHAPTER II. TOPOLOGY OF DIFFERENTIABLE MANI- FOLDS; 2.1 Complexes; 2.2 Singular homology; 2.3 Stokes' theorem; 2.4 De Rham cohomology; 2.5 Periods
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2.6 Decomposition theorem for compact Riemann surfaces2.7 The star isomorphism; 2.8 Harmonic forms. The operators d and ?; 2.9 Orthogonality relations; 2.10 Decomposition theorem for compact Riemannian manifolds; 2.11 Fundamental theorem; 2.12 Explicit expressions for d, d and ?; Exercises; CHAPTER III. CURVATURE AND HOMOLOGY OF RIEMANNIAN MANIFOLDS; 3.1 Some contributions of S. Bochner; 3.2 Curvature and betti numbers; 3.3 Derivations in a graded algebra; 3.4 Infinitesimal transformations; 3.5 The derivation ?(X); 3.6 Lie transformation groups; 3.7 Conformal transformations
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3.8 Conformal transformations (continued)3.9 Conformally flat manifolds; 3.10 Affline collineations; 3.11 Projective transformations; Exercises; CHAPTER IV. COMPACT LIE GROUPS; 4.1 The Grassman algebra of a Lie group; 4.2 Invariant differential forms; 4.3 Local geometry of a compact semi-simple Lie group; 4.4 Harmonic forms on a compact semi-simple Lie group; 4.5 Curvature and betti numbers of a compact semi-simple Lie group G; 4.6 Determination of the betti numbers of the simple Lie groups; Exercises; CHAPTER V. COMPLEX MANIFOLDS; 5.1 Complex manifolds; 5.2 Almost complex manifolds
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5.3 Local hermitian geometry5.4 The operators L and A; 5.5 Kaehler manifolds; 5.6 Topology of a Kaehler manifold; 5.7 Effective forms on an hermitian manifold; 5.8 Holomorphic maps. Induced structures; 5.9 Examples of Kaehler manifolds; Exercises; CHAPTER VI. CURVATURE AND HOMOLOGY OF KAEHLER MANIFOLDS; 6.1 Holomorphic curvature; 6.2 The effect of positive Ricci curvature; 6.3 Deviation from constant holomorphic curvature; 6.4 Kaehler-Einstein spaces; 6.5 Holomorphic tensor fields; 6.6 Complex parallelisable manifolds; 6.7 Zero curvature; 6.8 Compact complex parallelisable manifolds
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6.9 A topological characterization of compact complex parallelisable manifolds6.10 d"-cohomology; 6.11 Complex imbedding; 6.12 Euler characteristic; 6.13 The effect of sufficiently many holomorphic differentials; 6.14 The vanishing theorems of Kodaira; Exercises; CHAPTER VII. GROUPS OF TRANSFORMATIONS OF KAEHLER AND ALMOST KAEHLER MANIFOLDS; 7.1 Infinitesimal holomorphic transformations; 7.2 Groups of holomorphic transformations; 7.3 Kaehler manifolds with constant Ricci scalar curvature; 7.4 A theorem on transitive groups of holomorphic transformations
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7.5 Infinitesimal conformal transformations. Automorphisms
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English
Weitere Ausg.:
ISBN 0-12-374562-4
Sprache:
Englisch
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