no. 1
The Dolbeault operator on Hermitian spin surfaces
[L'opérateur de Dolbeault sur les surfaces hermitiennes de spin]
Alexandrov, Bodgan1 ; Grantcharov, Gueo2 ; Ivanov, Stefan2
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, Tome 51 (2001) no. 1, pp. 221-235.

On démontre l'annulation du noyau de l'opérateur de Dolbeault sur la racine carrée du fibré canonique d'une surface hermitienne de spin avec courbure scalaire positive. On obtient des minorations pour la première valeur propre de cet opérateur, dans le cas où la courbure scalaire conforme est non-négative.

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.

DOI : 10.5802/aif.1822
Classification : 53C15, 53C25, 53B35
Keywords: hermitian surfaces, Dirac operator, Dolbeault operator, twistor spinors
Mot clés : surfaces hermitiennes, opérateur de Dirac, opérateur de Dolbeault, spineurs twisteurs
Alexandrov, Bodgan 1 ; Grantcharov, Gueo 2 ; Ivanov, Stefan 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) 
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     title = {The {Dolbeault} operator on {Hermitian} spin surfaces},
     journal = {Annales de l'Institut Fourier},
     pages = {221--235},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {51},
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     year = {2001},
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     mrnumber = {1821075},
     zbl = {0987.53011},
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Alexandrov, Bodgan; Grantcharov, Gueo; Ivanov, Stefan. The Dolbeault operator on Hermitian spin surfaces. Annales de l'Institut Fourier, Tome 51 (2001) no. 1, pp. 221-235. doi : 10.5802/aif.1822. http://archive.numdam.org/articles/10.5802/aif.1822/

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