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Characterizations of Model Manifolds by Means of Certain Differential Systems

Published online by Cambridge University Press:  20 November 2018

S. Pigola  and
M. Rimoldi
S. Pigola
Affiliation:
Dipartimento di Fisica e Matematica, Universitá dell’Insubria, 22100 Como, Italy
M. Rimoldi
Affiliation:
Dipartimento di Matematica, Universitá degli Studi di Milano, 20133 Milano, Italye-mail: stefano.pigola@uninsubria.ite-mail: michele.rimoldi@unimi.it
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Abstract

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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

53C20metric rigiditymodel manifoldsObata's type theorems
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 3 , 01 September 2012 , pp. 632 - 645
Copyright
Copyright © Canadian Mathematical Society 2012

References

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