Lectures in mathematics : Kyoto University

vol. 9

A differential geometric study on strongly pseudo-convex manifolds / by Noboru Tanaka
c1975

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Introduction 1
Preliminary remarks 8
I. Strongly pseudo-convex manifolds
§ 1. Partially complex manifolds 10
§ 2. Strongly pseudo-convex manifolds 22
§ 3. The canonical affine connections of strongly pseudo-convex manifolds 28
§ 4. The canonical connections of holomorphic vector bundles 37
II. The harmonic theory on strongly-convex manifolds
§ 5. The Laplacian 43
§ 6. The harmonic theory for the complex {C^q(M, E),$bar{∂}_E} 52
§ 7. The cohomology groups H^{p,q}(M) 58
§ 8. The cohomology groups H^{k-1,1}_*(M) and H^k_0(M) 64
§ 9. Differentiable families of compact strongly pseudo-convex manifolds 72
§ 10. Strongly pseudo-convex manifolds and isolated singular points 82
III. Normal strongly pseudo-convex manifolds
§ 11. Normal strongly pseudo-convex manifolds 93
§ 12. The double complex {B^{p,q}(M), ∂,$bar{∂}} 105
§ 13. Reduction theorems for the cohomology groups H^{p,q}_{(λ)}(M) and H^k_0(M) 121
Appendix
Linear differential systems 139

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