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Transactions of the American Mathematical Society

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Total mean curvature of immersed surfaces in $ E\sp{m}$


Author: Bang-yen Chen
Journal: Trans. Amer. Math. Soc. 218 (1976), 333-341
MSC: Primary 53C40
MathSciNet review: 0397623
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Abstract: Total mean curvature and value-distribution of mean curvature for certain pseudo-umbilical surfaces are studied.


References [Enhancements On Off] (What's this?)

  • [1] Bang-yen Chen, Geometry of submanifolds, Marcel Dekker, Inc., New York, 1973. Pure and Applied Mathematics, No. 22. MR 0353212
  • [2] -, On the total curvature of immersed manifolds. I, II, III, Amer. J. Math. 93 (1971), 148-162; ibid. 94 (1972), 799-809; ibid. 95 (1973), 636-642. MR 43 #3971; 47 #7660; 48 #12438.
  • [3] Shiing-shen Chern and Richard K. Lashof, On the total curvature of immersed manifolds, Amer. J. Math. 79 (1957), 306–318. MR 0084811
  • [4] Nicolaas H. Kuiper, Immersions with minimal total absolute curvature, Colloque Géom. Diff. Globale (Bruxelles, 1958) Centre Belge Rech. Math., Louvain, 1959, pp. 75–88. MR 0123280
  • [5] T. J. Willmore, Mean curvature of immersed surfaces, An. Şti. Univ. “All. I. Cuza” Iaşi Secţ. I a Mat. (N.S.) 14 (1968), 99–103 (English, with Romanian summary). MR 0238220

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0397623-6
Keywords: Total mean curvature, pseudo-umbilical surfaces, Clifford torus, real projective plane, normal connection, Laplace's equation
Article copyright: © Copyright 1976 American Mathematical Society