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