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On the deformation of the tangent m-plane of a

Published online by Cambridge University Press:  20 January 2009

E. T. Davies
E. T. Davies
Affiliation:
King's College, London, W.C. 2.
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Schouten and van Kampen (1) have studied the deformation of a . Applying the methods of that paper to the tangent vectors , which exist by hypothesis at all points of a certain region Vm′ (m′ > m) of Vn, we shall have

Whence we define the differentials

In the application of the to the lower index is treated as an ordinal index only. We shall not be concerned with any extension of the to indices other than those of the general Vb (see 1, equ. 3.24).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 5 , Issue 4 , September 1938 , pp. 202 - 206
Copyright
Copyright © Edinburgh Mathematical Society 1938

References

1.Schouten, J. A. and van Kampen, E. R., “Beiträge zur Theorie der Deformation,” Prace Mat. Fiz. Warszawa, 41 (1933), 1–19.Google Scholar
2.Hayden, H. A., “Deformations of a curve in a Riemannian space,” Proc. London Math. Soc. (2), 32 (1931), 321–336.CrossRefGoogle Scholar
3.Cartan, E., “Leçons sur la Géométrie des Espaces de Riemann,” Paris, Gauthier-Villars, 1928.Google Scholar
4.Davies, E. T., “On the second and third fundamental forms of a sub-space,” Journal London Math. Soc., 12 (1937), 290–295.CrossRefGoogle Scholar