References
Almgren, F.: Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem. Ann. of Math.84, 277–292 (1966)
Cartan, E.: Familles de surfaces isoparamétriques dans les espaces à courbure constante, Oeuvres complètes. Part III, Vol.2, 1431–1445 (1955).
Chern, S.S.: Differential Geometry; its past and future. Actes Congres. Intern. Math. Tôme1, 41–53 (1970)
Chern, S.S., Do Carmo, M., Kobayashi, S.: Minimal submanifolds of a sphere with second fundamental form of constant length. Functional analysis and related fields. Proceedings of a Conference in Honour of H. Stone. 59–75. Berlin-Heidelberg-New York: Springer 1970
Eells, J., Sampson, H.: Harmonic mappings of Riemannian manifolds. Amer. J. Math.86, 109–160 (1964)
Erbacher, J.: Isometric immersions of constant mean curvature and triviality of the normal connection. Nagoya Math. J.45, 139–165 (1971)
Hopf, H.: Über Flächen mit einer Relation zwischen den Hauptkrümmungen. Math. Nachr.4, 232–249 (1951)
Hsiang, W.-Y.: On compact homogeneous minimal submanifolds. Proc. Nat. Acad. Sci. USA56, 5–6 (1966)
Kobayashi, S., Nomizu, K.: Foundations of differential geometry, Vols. I–II. New York: John Wiley and Sons 1963 and 1969
Matsushima, Y.: Vector bundle valued harmonic forms and immersions of Riemannian manifolds. Osaka J. Math.8, 1–13 (1971)
Moore, J.D.: Isometric immersions of Riemannian products. J. Diff. Geometry5, 159–168 (1971)
Myers, S.B.: Curvature of closed hypersurfaces and non-existence of closed minimal hypersurfaces. Trans. Amer. Math. Soc.71, 211–217 (1951)
Nomizu, K.: On the spaces of generalized curvature tensor fields and second fundamental forms. Osaka J. Math.8, 21–28 (1971)
Nomizu, K., Smyth, B.: A formula of Simons' type and hypersurfaces of constant mean curvature. J. Diff. Geometry3, 367–377 (1969)
Ruh, E.A.: Asymptotic behaviour of non-parametric minimal surfaces. J. Diff. Geometry4, 509–513 (1970)
Ruh, E.A.: Minimal immersions of 2-spheres inS 4, Proc. Amer. Math. Soc.28, 219–222 (1971)
Ruh, E.A., Vilms, J.: The tension field of the Gauss map. Trans. Amer. Math. Soc.149, 569–573 (1970)
Struik, D.J.: Lectures on classical differential geometry, second edition. Reading, Mass.: Addison-Wesley 1961
Süss, W.: Zur relativen Differentialgeometrie V, Tôhoku. Math. J.31, 202–209 (1929)
Takahashi, T.: Minimal immersions of Riemannian manifolds. J. Math. Soc. Japan18, 380–385 (1966)
Author information
Authors and Affiliations
Additional information
This work was partially supported by the National Science Foundation.
Rights and permissions
About this article
Cite this article
Smyth, B. Submanifolds of constant mean curvature. Math. Ann. 205, 265–280 (1973). https://doi.org/10.1007/BF01362697
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01362697