On compact holomorphically pseudosymmetric Kählerian manifolds

• Autorzy: Zbigniew Olszak
• Języki publikacji: EN

Abstrakty

EN

For compact Kählerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct examples of non-compact essentially holomorphically pseudosymmetric Kählerian manifolds. These examples show that the compactness assumption cannot be omitted in the above stated theorem. Recently, the first examples of compact, simply connected essentially holomorphically pseudosymmetric Kählerian manifolds are discovered in [4]. In these examples, the structure functions change their signs on the manifold.

Słowa kluczowe

EN

Kählerian manifold; Semisymmetry; Holomorphic pseudosymmetry

Kategorie tematyczne

• 53C55: Hermitian and K\"ahlerian manifolds
• 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 3
• Strony: 442-451

Daty

wydano

2009-09-01

online

2009-08-12

Twórcy

autor

Zbigniew Olszak

• Wrocław University of Technology

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0023-6