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On the Cartan-Norden theorem for affine Kähler immersions

100%

Robaszewska M.

Annales Polonici Mathematici

2000

tom 75

nr 1

69-77

In [O2] the Cartan-Norden theorem for real affine immersions was proved without the non-degeneracy assumption. A similar reasoning applies to the case of affine Kähler immersions with an anti-complex shape operator, which allows us to weaken the assumptions of the theorem given in [NP]. We need only require the immersion to have a non-vanishing type number everywhere on M.

On compact holomorphically pseudosymmetric Kählerian manifolds

80%

Olszak Z.

Open Mathematics

2009

tom 7

nr 3

442-451

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Open Mathematics

1 Olszak Z.

1 Robaszewska M.

1 2009

1 2000

Wyniki wyszukiwania

On the Cartan-Norden theorem for affine Kähler immersions

On compact holomorphically pseudosymmetric Kählerian manifolds