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 -solutions of a large class of differential inequalities. Further applications of the technique are also given.
Some characterizations of space-forms / Stefano Pigola, Marco Rigoli, A.G. Setti. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 359:4(2007), pp. 1817-1828. [10.1090/S0002-9947-06-04091-8]
Some characterizations of space-forms
M. Rigoli;
2007
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 -solutions of a large class of differential inequalities. Further applications of the technique are also given.
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