Nous étudions les métriques riemanniennes holomorphes sur les variétés complexes compactes de dimension . Nous montrons que, contrairement au cas réel, une métrique riemannienne holomorphe possède un “grand” pseudo-groupe d’isométries locales. Ceci implique qu’une telle métrique n’existe pas sur les variétés complexes compactes simplement connexes de dimension .
We study holomorphic Riemannian metrics on compact complex threefolds. We show that, contrary to the situation in the real domain, a holomorphic Riemannian metric admits a "big" pseudogroup of local isometries. It follows that compact complex simply connected threefolds do not admit any holomorphic Riemannian metric.
Mot clés : variétés complexes, métriques riemanniennes holomorphes, théorie algébrique des invariants, pseudo-groupe d'isométries locales
Keywords: complex manifolds, holomorphic riemannian metrics, algebraic theory of invariants, pseudogroup of local isometries
@article{AIF_2001__51_6_1663_0, author = {Dumitrescu, Sorin}, title = {M\'etriques riemanniennes holomorphes en petite dimension}, journal = {Annales de l'Institut Fourier}, pages = {1663--1690}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {51}, number = {6}, year = {2001}, doi = {10.5802/aif.1870}, mrnumber = {1871285}, zbl = {1016.53051}, language = {fr}, url = {http://archive.numdam.org/articles/10.5802/aif.1870/} }
TY - JOUR AU - Dumitrescu, Sorin TI - Métriques riemanniennes holomorphes en petite dimension JO - Annales de l'Institut Fourier PY - 2001 SP - 1663 EP - 1690 VL - 51 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1870/ DO - 10.5802/aif.1870 LA - fr ID - AIF_2001__51_6_1663_0 ER -
%0 Journal Article %A Dumitrescu, Sorin %T Métriques riemanniennes holomorphes en petite dimension %J Annales de l'Institut Fourier %D 2001 %P 1663-1690 %V 51 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1870/ %R 10.5802/aif.1870 %G fr %F AIF_2001__51_6_1663_0
Dumitrescu, Sorin. Métriques riemanniennes holomorphes en petite dimension. Annales de l'Institut Fourier, Tome 51 (2001) no. 6, pp. 1663-1690. doi : 10.5802/aif.1870. http://archive.numdam.org/articles/10.5802/aif.1870/
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