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Rotational hypersurfaces of space forms with constant scalar curvature

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Abstract

LetM be a complete rotational hypersurface of a space form with constant scalar curvatureS. In this paper we classify these hypersurfaces in the cases ofR n andH n, determine the admissible values ofS in each of the three spaces and give a geometrical description of the hypersurfaces according to the values ofS. In the case ofS n we find examples of embedded hypersurfaces with constantS∈(n−2/n−1, 1), which are not isometric to product of spheres.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Pernambuco, 50739, Recife, PE, (Brazil)

    Maria Luiza Leite

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  1. Maria Luiza Leite
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research partially supported by CNPq-Brazil

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Leite, M.L. Rotational hypersurfaces of space forms with constant scalar curvature. Manuscripta Math 67, 285–304 (1990). https://doi.org/10.1007/BF02568434

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  • DOI: https://doi.org/10.1007/BF02568434

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