The Dolbeault operator on Hermitian spin surfaces

Bodgan Alexandrov[1]; Gueo Grantcharov[2]; Stefan Ivanov[2]

  • [1] Humboldt University, Institute for Mathematics, Rudower Chaussee 25, 10099 Berlin (Allemagne)
  • [2] University of Sofia, Faculty of Mathematics and Informatics, Department of Geometry, 5 James Bourchier Blvd, 1126 Sofia (Bulgarie)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 1, page 221-235
  • ISSN: 0373-0956

Abstract

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We prove the vanishing of the kernel of the Dolbeault operator of the square root of the canonical line bundle of a compact Hermitian spin surface with positive scalar curvature. We give lower estimates of the eigenvalues of this operator when the conformal scalar curvature is non -negative.

How to cite

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Alexandrov, Bodgan, Grantcharov, Gueo, and Ivanov, Stefan. "The Dolbeault operator on Hermitian spin surfaces." Annales de l’institut Fourier 51.1 (2001): 221-235. <http://eudml.org/doc/115910>.

@article{Alexandrov2001,
abstract = {We prove the vanishing of the kernel of the Dolbeault operator of the square root of the canonical line bundle of a compact Hermitian spin surface with positive scalar curvature. We give lower estimates of the eigenvalues of this operator when the conformal scalar curvature is non -negative.},
affiliation = {Humboldt University, Institute for Mathematics, Rudower Chaussee 25, 10099 Berlin (Allemagne); University of Sofia, Faculty of Mathematics and Informatics, Department of Geometry, 5 James Bourchier Blvd, 1126 Sofia (Bulgarie); University of Sofia, Faculty of Mathematics and Informatics, Department of Geometry, 5 James Bourchier Blvd, 1126 Sofia (Bulgarie)},
author = {Alexandrov, Bodgan, Grantcharov, Gueo, Ivanov, Stefan},
journal = {Annales de l’institut Fourier},
keywords = {hermitian surfaces; Dirac operator; Dolbeault operator; twistor spinors; Hermitian surface},
language = {eng},
number = {1},
pages = {221-235},
publisher = {Association des Annales de l'Institut Fourier},
title = {The Dolbeault operator on Hermitian spin surfaces},
url = {http://eudml.org/doc/115910},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Alexandrov, Bodgan
AU - Grantcharov, Gueo
AU - Ivanov, Stefan
TI - The Dolbeault operator on Hermitian spin surfaces
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 1
SP - 221
EP - 235
AB - We prove the vanishing of the kernel of the Dolbeault operator of the square root of the canonical line bundle of a compact Hermitian spin surface with positive scalar curvature. We give lower estimates of the eigenvalues of this operator when the conformal scalar curvature is non -negative.
LA - eng
KW - hermitian surfaces; Dirac operator; Dolbeault operator; twistor spinors; Hermitian surface
UR - http://eudml.org/doc/115910
ER -

References

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