Hermitian spin surfaces with small eigenvalues of the Dolbeault operator
Annales de l'Institut Fourier, Volume 54 (2004) no. 7, p. 2437-2453
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
Nous étudions les variétés hermitiennes de spin avec courbure scalaire conforme positive sur lesquelles la première valeur propre de l'opérateur de Dolbeault est la plus petite possible. On montre qu'une telle surface est une surface réglée, ou bien une surface de Hopf. Nous donnons une classification complète des surfaces réglées avec cette propriété. Pour les surfaces de Hopf on obtient une classification partielle et quelques exemples.
DOI : https://doi.org/10.5802/aif.2085
Classification:  53C55,  32J15
Keywords: Hermitian surface, locally conformally Kähler metric, ruled surface, Hopf surface
@article{AIF_2004__54_7_2437_0,
     author = {Alexandrov, Bogdan},
     title = {Hermitian spin surfaces with small eigenvalues of the Dolbeault operator},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {7},
     year = {2004},
     pages = {2437-2453},
     doi = {10.5802/aif.2085},
     zbl = {1083.53067},
     mrnumber = {2139699},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2004__54_7_2437_0}
}
Alexandrov, Bogdan. Hermitian spin surfaces with small eigenvalues of the Dolbeault operator. Annales de l'Institut Fourier, Volume 54 (2004) no. 7, pp. 2437-2453. doi : 10.5802/aif.2085. http://www.numdam.org/item/AIF_2004__54_7_2437_0/

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