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Holomorphic Vector Fields on Compact Kähler Manifolds
Y. Matsushima
A co-publication of the AMS and CBMS.
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CBMS Regional Conference Series in Mathematics
1971; 38 pp; softcover
Number: 7
ISBN-10: 0-8218-1656-X
ISBN-13: 978-0-8218-1656-1
List Price: US$20
Member Price: US$16
All Individuals: US$16
Order Code: CBMS/7
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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
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