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

Maria Robaszewska. "A local characterization of affine holomorphic immersions with an anti-complex and ∇-parallel shape operator." Annales Polonici Mathematici 78.1 (2002): 59-84. <http://eudml.org/doc/280549>.

@article{MariaRobaszewska2002,
abstract = {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 $ℂ^\{n+1\}$.},
author = {Maria Robaszewska},
journal = {Annales Polonici Mathematici},
keywords = {affine holomorphic immersion; affine Kaehler connection; anti-complex shape operator; parallel shape operator},
language = {eng},
number = {1},
pages = {59-84},
title = {A local characterization of affine holomorphic immersions with an anti-complex and ∇-parallel shape operator},
url = {http://eudml.org/doc/280549},
volume = {78},
year = {2002},
}

TY - JOUR
AU - Maria Robaszewska
TI - A local characterization of affine holomorphic immersions with an anti-complex and ∇-parallel shape operator
JO - Annales Polonici Mathematici
PY - 2002
VL - 78
IS - 1
SP - 59
EP - 84
AB - 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 $ℂ^{n+1}$.
LA - eng
KW - affine holomorphic immersion; affine Kaehler connection; anti-complex shape operator; parallel shape operator
UR - http://eudml.org/doc/280549
ER -