The Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds
Annales de l'Institut Fourier, Volume 47 (1997) no. 5, p. 1345-1365

It is proved that if M is a weakly 1-complete Kähler manifold with only one end, then H c 1 (M,𝒪)=0 or there exists a proper holomorphic mapping of M onto a Riemann surface.

On démontre que si M est une variété kählérienne faiblement 1-complète avec un seul bout, alors H c 1 (M,𝒪)=0 ou bien il existe une application holomorphe propre de M sur une surface de Riemann.

@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {47},
     number = {5},
     year = {1997},
     pages = {1345-1365},
     doi = {10.5802/aif.1602},
     zbl = {0904.32008},
     mrnumber = {99e:32012},
     language = {en},
     url = {http://www.numdam.org/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, Volume 47 (1997) no. 5, pp. 1345-1365. doi : 10.5802/aif.1602. http://www.numdam.org/item/AIF_1997__47_5_1345_0/

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