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Submanifolds of Real Space Forms

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Geometry of Hypersurfaces

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Abstract

In this chapter, we review the basic theory of submanifolds of real space forms needed for our in-depth treatment of isoparametric and Dupin hypersurfaces in later chapters. Topics treated include focal sets, parallel hypersurfaces, tubes, tight and taut immersions, the relationship between taut and Dupin submanifolds, and the standard embeddings of projective spaces.

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  1. Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA, USA

    Thomas E. Cecil

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada

    Patrick J. Ryan

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  1. Thomas E. Cecil
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© 2015 Thomas E. Cecil and Patrick J. Ryan

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Cecil, T.E., Ryan, P.J. (2015). Submanifolds of Real Space Forms. In: Geometry of Hypersurfaces. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3246-7_2

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