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On singularities of submanifolds of higher dimensional Euclidean spaces. (English) Zbl 0187.18903

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[1] Baker, H. F., Principle of Geometry VI (1960), New York: Fredrick Ungar Publishing Company, New York
[2] Boerner, H., Representations of Groups, 127-130 (1963), Amsterdam: North Holland Publishing Company, Amsterdam · Zbl 0112.26301
[3] Chern, S. S., On a theorem of algebra and its geometrical application, Journal of the Indian Mathematical Society, 8, 29-36 (1944) · Zbl 0060.38201
[4] Chern, S. S.; Spanier, E., A theorem on orientable surfaces in four dimensional space, Commentarii Mathematici Helvetici, 25, 205-209 (1951) · Zbl 0043.38403
[5] Eisenhart, L. P., Minimal surfaces in Euclidean four space, American Journal of Mathematics, 34, 215-236 (1912) · JFM 43.0732.01
[6] Feldman, E. A., Geometry of immersions I, Transaction of the American Mathematical Society, 120, 185-224 (1965) · Zbl 0137.17803
[7] Feldman, E. A., Geometry of immersions II, Transaction of the American Mathematical Society, 125, 181-315 (1966) · Zbl 0156.42401
[8] Feldman, E. A., On parabolic and umbilic points of immersed hypersurfaces, Transactions of the American Mathematical Society, 127, 1-28 (1967) · Zbl 0147.21304
[9] Kommerell, K., Riemannsche Flächen in ebenen Raum von vier Dimensionen, Math. Ann., 60, 546-596 (1905) · JFM 36.0717.05
[10] Lane, E. P., Projective Differential Geometry of Curves and Surfaces (1932), Chicago: University of Chicago Press, Chicago · JFM 58.0789.01
[11] Lashof, R.; Smale, S., On the immersion of manifolds in Euclidean space, Annals of Mathematics, 69, 562-582 (1958) · Zbl 0097.38805
[12] Palais, R. S., A global formulation of the Lie theory of transformation groups (1957), Memoirs: American Mathematical Society, Memoirs · Zbl 0178.26502
[13] W. Pohl,Some integral formulas for space curves and their generalization, to appear in American Journal of Mathematics.
[14] Semple, J. G.; Roth, L., Introduction to Algebraic Geometry, 128-136 (1944), Oxford: Oxford University Press, Oxford
[15] Whitney, H., The self-intersections of a smooth n-manifold in 2n-space, Annals of Mathematics, 45, 220-246 (1944) · Zbl 0063.08237
[16] J. H. White,Self-linking and the Gauss integral in higher dimensions, Thesis, University of Minnesota, (1968), mimeographed.
[17] Moore, C. L. E.; Wilson, E. B., Differential geometry of two-dimensional surfaces in hyperspaces, Proceedings of the American Academy of Arts and Sciences, 52, 267-368 (1916)
[18] Y. C. Wong,A new curvature theory for surfaces in a Euclidean 4-space, Commentarii Mathematii Helvetici, 26 (1952). · Zbl 0048.15102
[19] Wong, Y. C., Contributions to the theory of surfaces in a 4-space of constant curvature, Transactions of the American Mathematical Society, 59, 467-507 (1946) · Zbl 0060.38605
[20] Wong, Y. C., Fields of isocline tangent along a curve in a Euclidean 4-space, Tohoku Mathematical Journal, 3, 322-329 (1951) · Zbl 0045.24701
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