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On Two Parameter Envelopes of n-Spheres in a Real Spaces Form

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Abstract

In this work we are mainly concerned with the study of special 2-parameter envelopes M n (n≥ 4) of n-spheres in a simply connected space form Q n+1 c (c = 0, 1 or −1) which satisfy the Weingarten relation A + BH + CK = 0 between the mean curvature H and the Gauss–Kronecker curvature K of the immersion x : M n → Q n+1 c , where A, B and C are real constants; such a relation includes the case H constant.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de São, Paulo, SP, Brazil, 05315-970

    A. C. Asperti & M. B. Chaves

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  1. A. C. Asperti
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  2. M. B. Chaves
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Asperti, A.C., Chaves, M.B. On Two Parameter Envelopes of n-Spheres in a Real Spaces Form. Geometriae Dedicata 75, 301–316 (1999). https://doi.org/10.1023/A:1005171620545

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  • DOI: https://doi.org/10.1023/A:1005171620545

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