The Dolbeault operator on Hermitian spin surfaces
[L'opérateur de Dolbeault sur les surfaces hermitiennes de spin]
Alexandrov, Bodgan ; Grantcharov, Gueo ; Ivanov, Stefan
Annales de l'Institut Fourier, Tome 51 (2001), p. 221-235 / Harvested from Numdam
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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.

Publié le : 2001-01-01
DOI : https://doi.org/10.5802/aif.1822
Classification:  53C15,  53C25,  53B35
Mots clés: surfaces hermitiennes, opérateur de Dirac, opérateur de Dolbeault, spineurs twisteurs 
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     author = {Alexandrov, Bodgan and Grantcharov, Gueo and Ivanov, Stefan},
     title = {The Dolbeault operator on Hermitian spin surfaces},
     journal = {Annales de l'Institut Fourier},
     volume = {51},
     year = {2001},
     pages = {221-235},
     doi = {10.5802/aif.1822},
     mrnumber = {1821075},
     zbl = {0987.53011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2001__51_1_221_0}
}

Alexandrov, Bodgan; Grantcharov, Gueo; Ivanov, Stefan. The Dolbeault operator on Hermitian spin surfaces. Annales de l'Institut Fourier, Tome 51 (2001) pp. 221-235. doi : 10.5802/aif.1822. http://gdmltest.u-ga.fr/item/AIF_2001__51_1_221_0/

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