no. 3
Holomorphic Riemannian metric and the fundamental group
[Métrique riemannienne holomorphe et groupe fondamental]
Biswas, Indranil1 ; Dumitrescu, Sorin2
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
2 Université Côte d’Azur, CNRS, LJAD
Bulletin de la Société Mathématique de France, Tome 147 (2019) no. 3, pp. 455-468

We prove that compact complex manifolds bearing a holomorphic Riemannian metric have an infinite fundamental group.

Nous démontrons que les variétés complexes compactes admettant une métrique riemannienne holomorphe ont un groupe fondamental infini.

DOI : 10.24033/bsmf.2789
Classification : 53B30, 53C50, 53A55
Keywords: holomorphic Riemannian metric, algebraic dimension, Killing fields, fundamental group
Mots-clés : métrique riemannienne holomorphe, dimension algébrique, champs de Killing, groupe fondamental

Biswas, Indranil 1 ; Dumitrescu, Sorin 2

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
2 Université Côte d’Azur, CNRS, LJAD 
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     title = {Holomorphic {Riemannian} metric and the fundamental group},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {455--468},
     year = {2019},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {147},
     number = {3},
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Biswas, Indranil; Dumitrescu, Sorin. Holomorphic Riemannian metric and the fundamental group. Bulletin de la Société Mathématique de France, Tome 147 (2019) no. 3, pp. 455-468. doi: 10.24033/bsmf.2789

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