Some characterizations of space-forms

Pigola, Stefano; Rigoli, Marco; Setti, Alberto

doi:10.1090/S0002-9947-06-04091-8

Some characterizations of space-forms

Authors: Stefano Pigola, Marco Rigoli and Alberto G. Setti
Journal: Trans. Amer. Math. Soc. 359 (2007), 1817-1828
MSC (2000): Primary 53C21; Secondary 35J60, 35B05
DOI: https://doi.org/10.1090/S0002-9947-06-04091-8
Published electronically: November 3, 2006
Erratum: Tran. Amer. Math. Soc. 360 (2008), 3943-3944.
MathSciNet review: 2272150
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Abstract: Integral conditions on the traceless Ricci tensor are used to characterize Euclidean and hyperbolic spaces among complete, locally conformally flat manifolds of constant scalar curvature. The main tools are vanishing-type results for $L^{p}$ -solutions of a large class of differential inequalities. Further applications of the technique are also given.

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