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Characterizations of Model Manifolds by Means of Certain Differential Systems

  Published:2011-06-29
 Printed: Sep 2012
  • S. Pigola,
    Dipartimento di Fisica e Matematica, Universitá dell'Insubria, 22100 Como, Italy
  • M. Rimoldi,
    Dipartimento di Matematica, Universitá degli Studi di Milano, 20133 Milano, Italy
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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.
Keywords: metric rigidity, model manifolds, Obata's type theorems metric rigidity, model manifolds, Obata's type theorems
MSC Classifications: 53C20 show english descriptions Global Riemannian geometry, including pinching [See also 31C12, 58B20] 53C20 - Global Riemannian geometry, including pinching [See also 31C12, 58B20]
 

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