#### Lectures in mathematics : Kyoto University

##### vol. 9

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

c1975

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 |