References
J. Barta, Sur la vibration fondamentale d'une membrane. Comptes Rendus Acad. Sci.204, 472–473 (1937).
B.-Y. Chen, On the support functions and spherical submanifolds. Math. J. Okayama Univ.15, 15–23 (1971).
B.-Y. Chen, Submanifolds in a Euclidean hypersphere. Proc. Amer. Math. Soc.27, 627–628 (1971).
B.-Y.Chen, Total mean curvature and submanifolds of finite type. Singapore 1984.
K. P. Grotemeyer, Eine Kennzeichnende Eigenschaft der Affinsphären. Arch. Math.3, 307–310 (1952).
T. Hasanis andD. Koutroufiotis, Hypersurfaces with a constant support function. Arch. Math.57, 189–192 (1991).
H.Hopf, Differential geometry in the large, LNM1000, Berlin-Heidelberg-New York 1983.
R. Schneider, Eine Kennzeichnung der Kugel. Arch. Math.16, 235–239 (1965).
U. Simon, Probleme der lokalen und globalen mehrdimensionalen Differentialgeometrie. Manuscripta Math.2, 241–284 (1970).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gæde, L., Gravesen, J. & Markvorsen, S. A characterization of spheres, circles and cardioids. Arch. Math 60, 579–590 (1993). https://doi.org/10.1007/BF01236085
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01236085