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.
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.
Keywords: hermitian surfaces, Dirac operator, Dolbeault operator, twistor spinors
Mot clés : surfaces hermitiennes, opérateur de Dirac, opérateur de Dolbeault, spineurs twisteurs
@article{AIF_2001__51_1_221_0, author = {Alexandrov, Bodgan and Grantcharov, Gueo and Ivanov, Stefan}, 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}, number = {1}, year = {2001}, doi = {10.5802/aif.1822}, mrnumber = {1821075}, zbl = {0987.53011}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1822/} }
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 SP - 221 EP - 235 VL - 51 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1822/ DO - 10.5802/aif.1822 LA - en ID - AIF_2001__51_1_221_0 ER -
%0 Journal Article %A Alexandrov, Bodgan %A Grantcharov, Gueo %A Ivanov, Stefan %T The Dolbeault operator on Hermitian spin surfaces %J Annales de l'Institut Fourier %D 2001 %P 221-235 %V 51 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1822/ %R 10.5802/aif.1822 %G en %F AIF_2001__51_1_221_0
Alexandrov, Bodgan; Grantcharov, Gueo; Ivanov, Stefan. The Dolbeault operator on Hermitian spin surfaces. Annales de l'Institut Fourier, Volume 51 (2001) no. 1, pp. 221-235. doi : 10.5802/aif.1822. http://www.numdam.org/articles/10.5802/aif.1822/
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