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Annali di Matematica Pura ed Applicata

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

Some curvature properties of complex surfaces

  • Izu Vaisman
Article

Summary

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.

Keywords

Scalar Curvature Sectional Curvature Complex Surface Fundamental Form Curvature Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Nicola Zanichelli Editore 1982

Authors and Affiliations

  • Izu Vaisman
    • 1
  1. 1.HaifaIsraele

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