The Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds

Napier, Terence; Ramachandran, Mohan

doi:10.5802/aif.1602

Napier, Terence ; Ramachandran, Mohan

Annales de l'Institut Fourier, Tome 47 (1997) no. 5, pp. 1345-1365.

Résumé
Abstract

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.

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.

MR Zbl | 1 citation dans Numdam

DOI : 10.5802/aif.1602

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     author = {Napier, Terence and Ramachandran, Mohan},
     title = {The {Bochner-Hartogs} dichotomy for weakly 1-complete {K\"ahler} manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {1345--1365},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {47},
     number = {5},
     year = {1997},
     doi = {10.5802/aif.1602},
     mrnumber = {99e:32012},
     zbl = {0904.32008},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1602/}
}

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Napier, Terence; Ramachandran, Mohan. The Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds. Annales de l'Institut Fourier, Tome 47 (1997) no. 5, pp. 1345-1365. doi : 10.5802/aif.1602. http://www.numdam.org/articles/10.5802/aif.1602/

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