Abstract
This chapter is devoted to provide a modern presentation of Cartan’s classification of Euclidean hypersurfaces M n of dimension n ≥ 5 that admit nontrivial conformal deformations. Besides conformally flat hypersurfaces, the simplest examples are those that are conformally congruent to cylinders and rotation hypersurfaces over surfaces in \(\mathbb {R}^3\), and to cylinders over three-dimensional hypersurfaces of \(\mathbb {R}^4\) that are cones over surfaces in \(\mathbb {S}^3\). These examples are called conformally surface-like hypersurfaces.
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Dajczer, M., Tojeiro, R. (2019). Conformally Deformable Hypersurfaces. In: Submanifold Theory . Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9644-5_17
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DOI: https://doi.org/10.1007/978-1-4939-9644-5_17
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