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A characterization of totally umbilical hypersurfaces of a space form by geodesic mapping

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Ukrainian Mathematical Journal Aims and scope

The idea of considering the second fundamental form of a hypersurface as the first fundamental form of another hypersurface has found very useful applications in Riemannian and semi-Riemannian geometry, especially when trying to characterize extrinsic hyperspheres and ovaloids. Recently, T. Adachi and S. Maeda gave a characterization of totally umbilical hypersurfaces in a space form by circles. In our paper, we give a characterization of totally umbilical hypersurfaces of a space form by means of geodesic mapping.

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References

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 4, pp. 583–587, April, 2013.

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Canfes, E.Ö., Özdeğer, A. A characterization of totally umbilical hypersurfaces of a space form by geodesic mapping. Ukr Math J 65, 643–648 (2013). https://doi.org/10.1007/s11253-013-0801-y

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  • DOI: https://doi.org/10.1007/s11253-013-0801-y

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