Total mean curvature of immersed surfaces in $E^{m}$
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- by Bang-yen Chen PDF
- Trans. Amer. Math. Soc. 218 (1976), 333-341 Request permission
Abstract:
Total mean curvature and value-distribution of mean curvature for certain pseudo-umbilical surfaces are studied.References
- Bang-yen Chen, Geometry of submanifolds, Pure and Applied Mathematics, No. 22, Marcel Dekker, Inc., New York, 1973. MR 0353212 —, 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.
- Shiing-shen Chern and Richard K. Lashof, On the total curvature of immersed manifolds, Amer. J. Math. 79 (1957), 306–318. MR 84811, DOI 10.2307/2372684
- 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
- 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
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 218 (1976), 333-341
- MSC: Primary 53C40
- DOI: https://doi.org/10.1090/S0002-9947-1976-0397623-6
- MathSciNet review: 0397623