On démontre que si est une variété kählérienne faiblement 1-complète avec un seul bout, alors ou bien il existe une application holomorphe propre de sur une surface de Riemann.
It is proved that if is a weakly 1-complete Kähler manifold with only one end, then or there exists a proper holomorphic mapping of onto a Riemann surface.
@article{AIF_1997__47_5_1345_0, author = {Napier, Terence and Ramachandran, Mohan}, title = {The Bochner-Hartogs dichotomy for weakly 1-complete K\"ahler manifolds}, journal = {Annales de l'Institut Fourier}, volume = {47}, year = {1997}, pages = {1345-1365}, doi = {10.5802/aif.1602}, mrnumber = {99e:32012}, zbl = {0904.32008}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1997__47_5_1345_0} }
Napier, Terence; Ramachandran, Mohan. The Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds. Annales de l'Institut Fourier, Tome 47 (1997) pp. 1345-1365. doi : 10.5802/aif.1602. http://gdmltest.u-ga.fr/item/AIF_1997__47_5_1345_0/
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