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Total curvatures of geodesic spheres. (English) Zbl 0416.53025

53C20 Global Riemannian geometry, including pinching
53C65 Integral geometry
Full Text: DOI
[1] M.Berger, P.Gauduchon and E.Mazet, Le spectre d’une vari?t? riemannienne. LNM194, Berlin and New York 1971. · Zbl 0223.53034
[2] A. L.Besse, Manifolds all of whose geodesics are closed. Ergebnisse der Mathematik, vol.93, Berlin and New York 1978. · Zbl 0387.53010
[3] B.-Y.Chen, Geometry of submanifolds. Pure and applied Mathematics, New York 1973. · Zbl 0262.53036
[4] B.-Y. Chen, An invariant of conformal mappings. Proc. Amer. Math. Soc.40, 563-564 (1973). · Zbl 0266.53020
[5] B.-Y.Chen and L.Vanthecke, Differential geometry of geodesic spheres, to appear.
[6] S. S. Chern andR. K. Lashof, On the total curvature of immersed manifolds. Amer. J. Math.79, 306-318 (1957). · Zbl 0078.13901
[7] A. Gray, The volume of a small geodesic hall of a Riemannian manifold. Michigan Math. J.20, 329-344 (1973). · Zbl 0279.58003
[8] A. Gray andL. Vanhecke, Riemannian geometry as determined by the volumes of small geodesic balls. Acta Math.142, 157-198 (1979). · Zbl 0428.53017
[9] H. S. Ruse, A. G. Walker andT. J. Willmore, Harmonic spaces. Cremonese, Roma 1961.
[10] R. T. Waechter, On hearing the shape of a drum: An extension to higher dimensions. Proc. Cambridge Philos. Soc.72, 439-447 (1972). · Zbl 0266.52005
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