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

Annales Polonici Mathematici (2002)

- Volume: 78, Issue: 1, page 59-84
- ISSN: 0066-2216

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topMaria 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 -

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