Abstract
We construct a sequence of isometric embeddings of spherical spaceforms with cylcic fundamental groups. The standard sphere and Veronese embedding are the first two elements in this sequence. The embeddings are orbits under the unitary group and consequently the lengths of geometric quantities (like the 2nd fundamental form or the mean curvature vector) are constant.
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Pedit, F.J. Isometric embeddings of spherical spaceforms with cyclic fundamental groups. Manuscripta Math 64, 127–133 (1989). https://doi.org/10.1007/BF01160114
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DOI: https://doi.org/10.1007/BF01160114