We study the complex hypersurfaces 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 .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-1-7,
author = {Maria Robaszewska},
title = {A local characterization of affine holomorphic immersions with an anti-complex and [?]-parallel shape operator},
journal = {Annales Polonici Mathematici},
volume = {79},
year = {2002},
pages = {59-84},
zbl = {1003.53012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-1-7}
}
Maria Robaszewska. A local characterization of affine holomorphic immersions with an anti-complex and ∇-parallel shape operator. Annales Polonici Mathematici, Tome 79 (2002) pp. 59-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-1-7/