A consequence of the Riemannian Goldberg-Sachs theorem is the fact that the Kähler form of an Einstein Hermitian surface is an eigenform of the curvature operator. Referring to this property as -Einstein condition we obtain a complete classification of the compact locally homogeneous -Einstein Hermitian surfaces. We also provide large families of non-homogeneous -Einstein (but non-Einstein) Hermitian metrics on , , and on the product surface of two curves and whose genuses are greater than 1 and 0, respectively.
Le théorème de Goldberg-Sachs riemannien a pour conséquence le fait que toute surface complexe, hermitienne, d’Einstein satisfait la condition -Einstein disant que la forme de Kähler est forme propre de l’opérateur de courbure. Dans cet article nous obtenons la classification complète des surfaces hermitiennes localement homogènes qui satisfont la condition -Einstein précédente. Nous construisons aussi des exemples de métriques hermitiennes non homogènes qui sont -Einstein (mais non Einstein) sur , et sur le produit d’une courbe de genre supérieur à 0 et d’une courbe de genre supérieur à 1.
@article{AIF_1999__49_5_1673_0, author = {Apostolov, Vestislav and Mu\v{s}karov, Oleg}, title = {Weakly-Einstein hermitian surfaces}, journal = {Annales de l'Institut Fourier}, pages = {1673--1692}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {49}, number = {5}, year = {1999}, doi = {10.5802/aif.1734}, mrnumber = {2000h:53091}, zbl = {0937.53035}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1734/} }
TY - JOUR AU - Apostolov, Vestislav AU - Muškarov, Oleg TI - Weakly-Einstein hermitian surfaces JO - Annales de l'Institut Fourier PY - 1999 SP - 1673 EP - 1692 VL - 49 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1734/ DO - 10.5802/aif.1734 LA - en ID - AIF_1999__49_5_1673_0 ER -
%0 Journal Article %A Apostolov, Vestislav %A Muškarov, Oleg %T Weakly-Einstein hermitian surfaces %J Annales de l'Institut Fourier %D 1999 %P 1673-1692 %V 49 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1734/ %R 10.5802/aif.1734 %G en %F AIF_1999__49_5_1673_0
Apostolov, Vestislav; Muškarov, Oleg. Weakly-Einstein hermitian surfaces. Annales de l'Institut Fourier, Volume 49 (1999) no. 5, pp. 1673-1692. doi : 10.5802/aif.1734. http://archive.numdam.org/articles/10.5802/aif.1734/
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