Complex Product Manifolds Cannot be Negatively Curved

Seshadri, Harish; Zheng, Fangyang

Asian J. Math., Tome 12 (2008) no. 1, p. 145-150 / Harvested from Project Euclid

Résumé

We show that if M = X × Y is the product of two complex manifolds (of positive dimensions), then M does not admit any complete Kähler metric with bisectional curvature bounded between two negative constants. More generally, a locally-trivial holomorphic fibre-bundle does not admit such a metric.

Publié le : 2008-06-15
Classification: Kähler manifolds, product manifolds, bisectional curvature, negative curvature, 53B25, 53C40

@article{1213798138,
     author = {Seshadri, Harish and Zheng, Fangyang},
     title = {Complex Product Manifolds Cannot be Negatively Curved},
     journal = {Asian J. Math.},
     volume = {12},
     number = {1},
     year = {2008},
     pages = { 145-150},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1213798138}
}

Seshadri, Harish; Zheng, Fangyang. Complex Product Manifolds Cannot be Negatively Curved. Asian J. Math., Tome 12 (2008) no. 1, pp.  145-150. http://gdmltest.u-ga.fr/item/1213798138/