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Union Curves in a Subspace Vn of a Riemannian Vm

Published online by Cambridge University Press:  20 November 2018

M. K. Singal
M. K. Singal*
Affiliation:
Ramjas College, Delhi
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A union curve on a surface in a euclidean 3-space, relative to a given congruence is characterized by the property that its osculating plane at each point contains the ray of the congruence through that point. Springer (2) and Pan (1) have studied union curves in a hypersurface Vn of a Riemannian Vn+1. In the present paper we proceed to obtain the equations of union curves in a subspace Vn of a Riemannian Vm.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 101 - 105
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Pan, T. K., On a generalisation of the first curvature of a curve in a hypersurface of a Riemannian Space, Can. J. Math., 6 (1954), 210–216.Google Scholar
2. Springer, C. E., Union curves of a hypersurface, Can. J. Math. 2 (1950), 451–460.Google Scholar
3. Weatherburn, C. E., An introduction to Riemannian geometry and tensor calculus, Cambridge (1950).Google Scholar