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Bibliography
E. CARTAN, Leçons sur la Géométrie des Espaces de Riemann, Paris, Gauthier-Villars, 1928.
B.-y. CHEN, Geometry of Submanifolds, New York, Marcel Dekker, 1973.
B.-y. CHEN & T. NAGANO, Totally geodesic submanifolds of symmetric spaces, II, Duke Math. J. 45 (1978), 405–425; —, III, (to appear).
B.-y. CHEN & K. OGIUE, Some characterizations of complex space forms, Duke Math. J. 40 (1973), 797–799.
B.-y. CHEN & L. VERSTRAELEN, Hypersurfaces of symmetric spaces, Bull. Inst. Math. Academia Sinica, Memorial Issue Dedicated to H.C. Wang (1979).
S.I. GOLDBERG, The axiom of 2-spheres in Kaehler geometry, J. Differential Geometry 8 (1973), 177–179.
M. HARADA, On Kaehler manifolds satisfying the axiom of antiholomorphic 2-spheres, Proc. Amer. Math. Soc. 43 (1974), 186–189.
R.S. KULKARNI, A finite version of Schur’s theorem, Proc. Amer. Math. Soc. 53 (1975), 440–442.
D.S. LEUNG & K. NOMIZU, The axiom of spheres in Riemannian geometry, J. Differential Geometry 5 (1971), 487–489.
K. NOMIZU, Conditions for constancy of the holomorphic sectional curvature, J. Differential Geometry 8 (1973), 335–339.
Z. OLSZAK, Remarks on manifolds admitting totally umbilical hypersurfaces, Demonstratio Math. 11 (1978), 695–702.
J.A. SCHOUTEN, Ricci-Calculus, Berlin, Springer, 1954.
S. TACHIBANA & T. KASHIWADA, On a characterization of spaces of constant holomorphic curvature in terms of geodesic hypersurfaces, Kyungpook Math. J. 13 (1973), 109–119.
Y. TASHIRO & S. TACHIBANA, On Fubinian and C-Fubinian manifolds, Kōdai Math. Sem. Rep. 15 (1963), 176–183.
L. VANHECKE & T.J. WILLMORE, Umbilical hypersurfaces of Riemannian, Kaehler and Nearly Kaehler manifolds, J. Univ of Kuwait 4 (1977), 1–8.
K. YANO & I. MOGI, On real representations of Kaehlerian manifolds, Ann. of Math. 61 (1955).
K. YANO & Y. MUTO, Sur la théorie des espaces à connexion conforme normale et la gómétrie conforme des espaces de Riemann, Journal Fac. Sci., Imperial University of Tokyo, 4 (1941), 117–169.
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Chen, By., Verstraelen, L. (1981). Characterizations of space forms by hypersurfaces. In: Ferus, D., Kühnel, W., Simon, U., Wegner, B. (eds) Global Differential Geometry and Global Analysis. Lecture Notes in Mathematics, vol 838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088846
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DOI: https://doi.org/10.1007/BFb0088846
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