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Integral formulas and hyperspheres in a simply connected space form. (English) Zbl 0523.53053

MSC:
53C40 Global submanifolds
53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
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References:
[1] Irl Bivens, Codazzi tensors and reducible submanifolds, Trans. Amer. Math. Soc. 268 (1981), no. 1, 231 – 246. · Zbl 0474.53005
[2] Robert B. Gardner, The Dirichlet integral in differential geometry, Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 231 – 237.
[3] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, Cambridge, 1934. · JFM 60.0169.01
[4] Chuan-Chih Hsiung, Some integral formulas for closed hypersurfaces, Math. Scand. 2 (1954), 286 – 294. · Zbl 0057.14603
[5] Yoshihiro Tashiro, Complete Riemannian manifolds and some vector fields, Trans. Amer. Math. Soc. 117 (1965), 251 – 275. · Zbl 0136.17701
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