On the Cartan-Norden theorem for affine Kähler immersions

Maria Robaszewska

Annales Polonici Mathematici (2000)

  • Volume: 75, Issue: 1, page 69-77
  • ISSN: 0066-2216

Abstract

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In [O2] the Cartan-Norden theorem for real affine immersions was proved without the non-degeneracy assumption. A similar reasoning applies to the case of affine Kähler immersions with an anti-complex shape operator, which allows us to weaken the assumptions of the theorem given in [NP]. We need only require the immersion to have a non-vanishing type number everywhere on M.

How to cite

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Robaszewska, Maria. "On the Cartan-Norden theorem for affine Kähler immersions." Annales Polonici Mathematici 75.1 (2000): 69-77. <http://eudml.org/doc/208385>.

@article{Robaszewska2000,
abstract = {In [O2] the Cartan-Norden theorem for real affine immersions was proved without the non-degeneracy assumption. A similar reasoning applies to the case of affine Kähler immersions with an anti-complex shape operator, which allows us to weaken the assumptions of the theorem given in [NP]. We need only require the immersion to have a non-vanishing type number everywhere on M.},
author = {Robaszewska, Maria},
journal = {Annales Polonici Mathematici},
keywords = {Kählerian manifold; affine immersion; affine immersions},
language = {eng},
number = {1},
pages = {69-77},
title = {On the Cartan-Norden theorem for affine Kähler immersions},
url = {http://eudml.org/doc/208385},
volume = {75},
year = {2000},
}

TY - JOUR
AU - Robaszewska, Maria
TI - On the Cartan-Norden theorem for affine Kähler immersions
JO - Annales Polonici Mathematici
PY - 2000
VL - 75
IS - 1
SP - 69
EP - 77
AB - In [O2] the Cartan-Norden theorem for real affine immersions was proved without the non-degeneracy assumption. A similar reasoning applies to the case of affine Kähler immersions with an anti-complex shape operator, which allows us to weaken the assumptions of the theorem given in [NP]. We need only require the immersion to have a non-vanishing type number everywhere on M.
LA - eng
KW - Kählerian manifold; affine immersion; affine immersions
UR - http://eudml.org/doc/208385
ER -

References

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  1. [NPP] K. Nomizu, U. Pinkall and F. Podesta, On the geometry of affine Kähler immersions, Nagoya Math. J. 120 (1990), 205-222. Zbl0701.53038
  2. [NP] K. Nomizu and F. Podesta, On the Cartan-Norden theorem for affine Kähler immersions, Nagoya Math. J. 121 (1991), 127-135. Zbl0719.53029
  3. [O1] B. Opozda, On some properties of the curvature and Ricci tensors in complex affine geometry, Geom. Dedicata 55 (1995), 141-163. Zbl0840.53009
  4. [O2] B. Opozda, On the Cartan-Norden theorem, Math. Z. 226 (1997), 309-316. Zbl0973.53510

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