Geometriae Dedicata

, Volume 189, Issue 1, pp 59–78 | Cite as

On rigidity of generalized conformal structures

Original Paper
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Abstract

The classical Liouville Theorem on conformal transformations determines local conformal transformations on the Euclidean space of dimension \({\ge }3\) . Its natural adaptation to the general framework of Riemannian structures is the 2-rigidity of conformal transformations, that is such a transformation is fully determined by its 2-jet at any point. We prove here a similar rigidity for generalized conformal structures defined by giving a one parameter family of metrics (instead of scalar multiples of a given one) on each tangent space.

Keywords

Space of metrics Conformal structure Generalized conformal structure Lightlike metric Rigidity Liouville Thoerem 

Mathematics Subject Classification

53A30 53C24 53C10 
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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of MathematicsUSTOranAlgeria
  2. 2.CNRS, UMPA, ENSLyonFrance

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