On the Curvature of Compact Hermitian Manifolds.

Shing-Tung Yau

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3-manifolds with(out) metrics of nonpositive curvature.

Bernhard Leeb (1995)

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Hermitian Manifolds of Pointwise Constant Antiholomorphic Sectional Curvatures

Ganchev, Georgi, Kassabov, Ognian (2007)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 53B35, Secondary 53C50. In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.

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V. Schroeder, M.T. Anderson (1986)

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On a Bianchi-type identity for the almost hermitian manifolds

Giovanni Battista Rizza (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Almost hermitian manifolds, whose Riemann curvature tensor satisfies an almost complex Bianchi-type identity, are considered. Some local and global theorems are proved. The special cases of parakähler manifolds and of Kähler manifolds are examined.