Reviews

"Treats in a readable fashion two topics from the theory of vector fields."

-- James B. Carrell, Mathematical Reviews

Table of Contents

• Kähler geometry
• Harmonic forms
• The 1-form of type \((0, 1)\) corresponding to a holomorphic vector field
• Laplacian \(\Delta_f^{\prime\prime}\)
• An integral formula
• The case \(C_1(M)\leq 0\)
• The case \(C_1(M)\geq 0\)
• Study of \(\mathbf a_f\)
• Theorems of Lichnerowicz
• A remark on holomorphic vector fields on projective algebraic manifolds
• The Albanese variety of a Kähler manifold and the Jacobi map
• The case of Hodge manifolds
• \(G\)-sheaves
• The action of Aut\(_0(M)\) on complex line bundles over \(M\)
• The Lie derivative of a complex line bundle
• The kernel of the homomorphism \(p_F\)
• Proof of the Blanchard Theorem
• Bibliography