Hermitian spin surfaces with small eigenvalues of the Dolbeault operator

Bogdan Alexandrov[1]

  • [1] Universität Greifswald, Institut für Mathemathik und Informatik, Friedrich-Ludwig-Jahn-Str. 15a, 17487 Greifswald (Allemagne)

Annales de l'Institut Fourier (2004)

  • Volume: 54, Issue: 7, page 2437-2453
  • ISSN: 0373-0956

Abstract

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We study the compact Hermitian spin surfaces with positive conformal scalar curvature on which the first eigenvalue of the Dolbeault operator of the spin structure is the smallest possible. We prove that such a surface is either a ruled surface or a Hopf surface. We give a complete classification of the ruled surfaces with this property. For the Hopf surfaces we obtain a partial classification and some examples

How to cite

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Alexandrov, Bogdan. "Hermitian spin surfaces with small eigenvalues of the Dolbeault operator." Annales de l'Institut Fourier 54.7 (2004): 2437-2453. <http://eudml.org/doc/116178>.

@article{Alexandrov2004,
abstract = {We study the compact Hermitian spin surfaces with positive conformal scalar curvature on which the first eigenvalue of the Dolbeault operator of the spin structure is the smallest possible. We prove that such a surface is either a ruled surface or a Hopf surface. We give a complete classification of the ruled surfaces with this property. For the Hopf surfaces we obtain a partial classification and some examples},
affiliation = {Universität Greifswald, Institut für Mathemathik und Informatik, Friedrich-Ludwig-Jahn-Str. 15a, 17487 Greifswald (Allemagne)},
author = {Alexandrov, Bogdan},
journal = {Annales de l'Institut Fourier},
keywords = {Hermitian surface; locally conformally Kähler metric; ruled surface; Hopf surface; Kähler metric; locally conformal Kähler metric},
language = {eng},
number = {7},
pages = {2437-2453},
publisher = {Association des Annales de l'Institut Fourier},
title = {Hermitian spin surfaces with small eigenvalues of the Dolbeault operator},
url = {http://eudml.org/doc/116178},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Alexandrov, Bogdan
TI - Hermitian spin surfaces with small eigenvalues of the Dolbeault operator
JO - Annales de l'Institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 7
SP - 2437
EP - 2453
AB - We study the compact Hermitian spin surfaces with positive conformal scalar curvature on which the first eigenvalue of the Dolbeault operator of the spin structure is the smallest possible. We prove that such a surface is either a ruled surface or a Hopf surface. We give a complete classification of the ruled surfaces with this property. For the Hopf surfaces we obtain a partial classification and some examples
LA - eng
KW - Hermitian surface; locally conformally Kähler metric; ruled surface; Hopf surface; Kähler metric; locally conformal Kähler metric
UR - http://eudml.org/doc/116178
ER -

References

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