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Krümmungsflächen von isometrischen Immersionen in Räume konstanter Krümmung. (German) Zbl 0319.53042


MSC:

53C40 Global submanifolds
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References:

[1] Chern, S. S., do Carmo, M., Kobayashi, S.: Minimal submanifolds of a sphere with second fundamental form of constant length. Functional analysis and related fields. Proceedings of a conference in honor of Professor Marshall Stone, 1968. Berlin, Heidelberg, New York: Springer 1970
[2] Erbacher, J.: Reduction of the codimension of an isometric immersion. J. Diff. Geometry5, 333-340 (1971) · Zbl 0221.53031
[3] Ferus, D.: On the type number of hypersurfaces in spaces of constant curvature. Math. Ann.187, 310-316 (1970) · Zbl 0191.52104 · doi:10.1007/BF01396461
[4] Henke, W.: Über die isometrische Fortsetzbarkeit isometrischer Immersionen der Standard-m-SphäreS m (? ? m+1 ) in ? m+2 . Math. Ann.219, 261-276 (1976) · Zbl 0311.53032 · doi:10.1007/BF01354287
[5] Henke, W.: Über die Existenz isometrischer Immersionen der Kodimension 2 von sphärischen Raumformen in Standard-Räume. Math. Ann.222, 89-95 (1976) · Zbl 0318.53053 · doi:10.1007/BF01418246
[6] Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0148.12601
[7] Kobayashi, S., Nomizu, K.: Foundations of differential geometry II. New York, London, Sydney: Interscience 1969 · Zbl 0175.48504
[8] Nomizu, K.: Some results in E. Cartans theory of isoparametric families of hypersurfaces. Bull. Amer. Math. Soc.79, 1184-1188 (1973) · Zbl 0275.53003 · doi:10.1090/S0002-9904-1973-13371-3
[9] O’Neill, B.: Umbilics of constant curvature immersions. Duke Math. J.32, 149-159 (1965) · Zbl 0134.39501 · doi:10.1215/S0012-7094-65-03213-8
[10] Otsuki, T.: On principal normal vector fields of submanifolds in a Riemannian manifold of constant curvature. J. Math. Soc. Japan22, 35-46 (1970) · Zbl 0182.24202 · doi:10.2969/jmsj/02210035
[11] Smyth, B.: Submanifolds of constant mean curvature. Math. Ann.205, 265-280 (1973) · Zbl 0262.53037 · doi:10.1007/BF01362697
[12] Walden, R.: Untermannigfaltigkeiten mit paralleler zweiter Fundamentalform in euklidischen Räumen und Sphären. manuscripta math.10, 91-102 (1973) · Zbl 0262.53038 · doi:10.1007/BF01677009
[13] Wolf, J. A.: Spaces of constant curvature. New York: McGraw-Hill 1967 · Zbl 0162.53304
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