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arXiv · 1411.5709

On Rigidity of Generalized Conformal Structures

Samir Bekkara·Abdelghani Zeghib
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Abstract

The classical Liouville Theorem on conformal transformations determines local conformal transformations on the Euclidean space of dimension $\geq 3$. 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.

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Samir Bekkara, Abdelghani Zeghib. 2014-11-20. On Rigidity of Generalized Conformal Structures. https://arxiv.org/abs/1411.5709

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