Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
E. CARTAN, LeƧons sur la GƩomƩtrie 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), 405ā425; ā, III, (to appear).
B.-y. CHEN & K. OGIUE, Some characterizations of complex space forms, Duke Math. J. 40 (1973), 797ā799.
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), 177ā179.
M. HARADA, On Kaehler manifolds satisfying the axiom of antiholomorphic 2-spheres, Proc. Amer. Math. Soc. 43 (1974), 186ā189.
R.S. KULKARNI, A finite version of Schurās theorem, Proc. Amer. Math. Soc. 53 (1975), 440ā442.
D.S. LEUNG & K. NOMIZU, The axiom of spheres in Riemannian geometry, J. Differential Geometry 5 (1971), 487ā489.
K. NOMIZU, Conditions for constancy of the holomorphic sectional curvature, J. Differential Geometry 8 (1973), 335ā339.
Z. OLSZAK, Remarks on manifolds admitting totally umbilical hypersurfaces, Demonstratio Math. 11 (1978), 695ā702.
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), 109ā119.
Y. TASHIRO & S. TACHIBANA, On Fubinian and C-Fubinian manifolds, KÅdai Math. Sem. Rep. 15 (1963), 176ā183.
L. VANHECKE & T.J. WILLMORE, Umbilical hypersurfaces of Riemannian, Kaehler and Nearly Kaehler manifolds, J. Univ of Kuwait 4 (1977), 1ā8.
K. YANO & I. MOGI, On real representations of Kaehlerian manifolds, Ann. of Math. 61 (1955).
K. YANO & Y. MUTO, Sur la thĆ©orie des espaces Ć connexion conforme normale et la gĆ³mĆ©trie conforme des espaces de Riemann, Journal Fac. Sci., Imperial University of Tokyo, 4 (1941), 117ā169.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
Ā© 1981 Springer-Verlag
About this paper
Cite this paper
Chen, By., Verstraelen, L. (1981). Characterizations of space forms by hypersurfaces. In: Ferus, D., KĆ¼hnel, 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
Download citation
DOI: https://doi.org/10.1007/BFb0088846
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10285-4
Online ISBN: 978-3-540-38419-9
eBook Packages: Springer Book Archive