DIFFERENTIAL ANALYSIS ON COMPLEX MANIFOLDS

By M. LUIRR

C O N T E N T S CHAPTER I MANIFOLDS AND VECTOR BUNDLES 1 MANIFOLDS 2 VECTOR BUNDLES 3 ALMOST COMPLEX MANIFOLDS AND THE ¯?-OPERATOR CHAPTER II SHEAF THEORY 1 PRESHEAVES AND SHEAVES 2 RESOLUTIONS OF SHEAVES 3 COHOMOLOGY THEORY 4 ?CECH COHOMOLOGY WITH COEF?CIENTS IN A SHEAF CHAPTER III DIFFERENTIAL GEOMETRY 1 HERMITIAN DIFFERENTIAL GEOMETRY 2 THE CANONICAL CONNECTION AND CURVATURE OF A HERMITIAN HOLOMORPHIC VECTOR BUNDLE 3 CHERN CLASSES OF DIFFERENTIABLE VECTOR BUNDLES 4 COMPLEX LINE BUNDLES CONTENTS CHAPTER IV ELLIPTIC OPERATOR THEORY 1 SOBOLEV SPACES 2 DIFFERENTIAL OPERATORS 3 PSEUDODIFFERENTIAL OPERATORS 4 A PARAMETRIX FOR ELLIPTIC DIFFERENTIAL OPERATORS 5 ELLIPTIC COMPLEXES CHAPTER V COMPACT COMPLEX MANIFOLDS 1 HERMITIAN EXTERIOR ALGEBRA ON A HERMITIAN VECTOR SPACE 2 HARMONIC THEORY ON COMPACT MANIFOLDS 3 REPRESENTATIONS OF SL(2, C) ON HERMITIAN EXTERIOR ALGEBRAS 4 DIFFERENTIAL OPERATORS ON A KÄHLER MANIFOLD 5 THE HODGE DECOMPOSITION THEOREM ON COMPACT KÄHLER MANIFOLDS 6 THE HODGE-RIEMANN BILINEAR RELATIONS ON A KÄHLER MANIFOLD CHAPTER VI KODAIRA’S PROJECTIVE EMBEDDING THEOREM 1 HODGE MANIFOLDS 2 KODAIRA’S VANISHING THEOREM 3 QUADRATIC TRANSFORMATIONS 4 KODAIRA’S EMBEDDING THEOREM