A local characterization of affine holomorphic immersions with an anti-complex and ∇-parallel shape operator

• Autorzy: Maria Robaszewska
• Języki publikacji: EN

Abstrakty

EN

We study the complex hypersurfaces $f:M^{(n)} → ℂ^{n+1}$ which together with their transversal bundles have the property that around any point of M there exists a local section of the transversal bundle inducing a ∇-parallel anti-complex shape operator S. We give a class of examples of such hypersurfaces with an arbitrary rank of S from 1 to [n/2] and show that every such hypersurface with positive type number and S ≠ 0 is locally of this kind, modulo an affine isomorphism of $ℂ^{n+1}$.

Kategorie tematyczne

• 53A15: Affine differential geometry
• 53C56: Other complex differential geometry
• 53B05: Linear and affine connections

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2002
• Tom: 78
• Numer: 1
• Strony: 59-84

Daty

wydano

2002

Twórcy

autor

Maria Robaszewska

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

Identyfikatory

DOI

10.4064/ap78-1-7