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

Maria Robaszewska (2002)

Annales Polonici Mathematici

We study the complex hypersurfaces f : M ( n ) 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 n + 1 .

A remark on semi-∇-flat functions

Wojciech Kozłowski (2006)

Annales Polonici Mathematici

We give a pointwise characterization of semi-∇-flat functions on an affine manifold (M,∇).

Affine maximal hypersurfaces

An-Min Li, Fang Jia (2005)

Banach Center Publications

This paper is part of the autumn school on "Variational problems and higher order PDEs for affine hypersurfaces". We discuss affine Bernstein problems and complete constant mean curvature surfaces in equiaffine differential geometry.

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