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References
Cecil, T.E., Ryan, P.J.: Focal sets of submanifolds. Pacific J. Math.78, 27–39 (1978)
Chern, S.S., Do Carmo, M., Kobayashi, S.: Minimal submanifolds of a sphere with second fundamental form of constant length. In: Functional analysis and related fields, pp. 59–75. Berlin, Heidelberg, New York: Springer 1970
Dombrowski, P.: On the geometry of the tangent bundle. J. reine angew. Math.210, 73–88 (1962)
Ferus, D.: On the completeness of nullity foliations. Mich. Math. J.18, 61–64 (1971)
Gromoll, D., Klingenberg, W., Meyer, W.: Riemannsche Geometrie im Großen. Lecture Notes in Mathematics, Vol. 55. Berlin, Heidelberg, New York: Springer 1968
Kobayashi, K.N., Nomizu, K.: Foundations of differential geometry. I, II. New York: Interscience 1963/69
Nomizu, K., Yano, K.: On circles and spheres in Riemannian geometry. Math. Ann.210, 163–170 (1974)
Nomizu, K.: Characteristic roots and vectors of a differentiable family of symmetric matrices. Linear and Multilinear Algebra1, 159–162 (1973)
Otsuki, T.: On principal normal vector fields of submanifolds in a Riemannian manifold of constant curvature. J. Math. Soc. Japan22, 35–46 (1970)
Palais, R.S.: A global formulation of the Lie theory of transformation groups. Mem. Amer. Math. Soc.22 (1957)
Reckziegel, H.: Krümmungsflächen von isometrischen Immersionen in Räume konstanter Krümmung. Math. Ann.223, 169–181 (1976)
Reckziegel, H.: On the completeness of curvature surfaces of an isometric immersion. J. Differential Geometry (to appear)
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Reckziegel, H. On the eigenvalues of the shape operator of an isometric immersion into a space of constant curvature. Math. Ann. 243, 71–82 (1979). https://doi.org/10.1007/BF01420208
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DOI: https://doi.org/10.1007/BF01420208