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arXiv · 2002.02551

Conformal infinitesimal variations of submanifolds

M. Dajczer·M. I. Jimenez
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Abstract

This paper belongs to the realm of conformal geometry and deals with Euclidean submanifolds that admit smooth variations that are infinitesimally conformal. Conformal variations of Euclidean submanifolds is a classical subject in differential geometry. In fact, already in 1917 Cartan classified parametrically the Euclidean hypersurfaces that admit nontrivial conformal variations. Our first main result is a Fundamental theorem for conformal infinitesimal variations. The second is a rigidity theorem for Euclidean submanifolds that lie in low codimension.

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M. Dajczer, M. I. Jimenez. 2020-02-06. Conformal infinitesimal variations of submanifolds. https://arxiv.org/abs/2002.02551

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