Annali di Matematica Pura ed Applicata

, Volume 132, Issue 1, pp 1–18 | Cite as

Some curvature properties of complex surfaces

  • Izu Vaisman


In this paper, we are investigating curvature properties of complex two-dimensional Hermitian manifolds, particularly in the compact case. To do this, we start with the remark that the fundamental form of such a manifold is integrable, and we use the analogy with the locally conformal KÄhler manifolds, which follows from this remark. Among the obtained results, we have the following: a compact Hermitian surface for which either the Riemannian curvature tensor satisfies the KÄhler symmetries or the Hermitian curvature tensor satisfies the Riemannian Bianchi identity is KÄhler; a compact Hermitian surface of constant sectional curvature is a flat KÄhler surface; a compact Hermitian surface M with nonnegative nonidentical zero holomorphie Hermitian bisectional curvature has vanishing plurigenera, c1(M) ⩾ 0, and no exceptional curves; a compact Hermitian surface with distinguished metric, and positive integral Riemannian scalar curvature has vanishing plurigenera, etc.


Scalar Curvature Sectional Curvature Complex Surface Fundamental Form Curvature Tensor 
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Copyright information

© Nicola Zanichelli Editore 1982

Authors and Affiliations

  • Izu Vaisman
    • 1
  1. 1.HaifaIsraele

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