On the Cartan-Norden theorem for affine Kähler immersions

• Autorzy: Maria Robaszewska
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Kählerian manifold; affine immersion

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 75
• Numer: 1
• Strony: 69-77

Daty

wydano

2000

otrzymano

1999-10-20

Twórcy

autor

Maria Robaszewska

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

• [NPP] K. Nomizu, U. Pinkall and F. Podesta, On the geometry of affine Kähler immersions, Nagoya Math. J. 120 (1990), 205-222.
• [NP] K. Nomizu and F. Podesta, On the Cartan-Norden theorem for affine Kähler immersions, Nagoya Math. J. 121 (1991), 127-135.
• [O1] B. Opozda, On some properties of the curvature and Ricci tensors in complex affine geometry, Geom. Dedicata 55 (1995), 141-163.
• [O2] B. Opozda, On the Cartan-Norden theorem, Math. Z. 226 (1997), 309-316.