We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. Along the way, we also discover new characterizations of space-forms. We next generalize results concerning metric rigidity via equations involving vector fields. © Canadian Mathematical Society 2011.
Pigola, S., Rimoldi, M. (2012). Characterizations of model manifolds by means of certain differential systems. CANADIAN MATHEMATICAL BULLETIN, 55(3), 632-645 [10.4153/CMB-2011-134-0].
Characterizations of model manifolds by means of certain differential systems
Pigola, S;RIMOLDI, MICHELE
2012
Abstract
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. Along the way, we also discover new characterizations of space-forms. We next generalize results concerning metric rigidity via equations involving vector fields. © Canadian Mathematical Society 2011.
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