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Subspaces of a Generalized Metric Space

Published online by Cambridge University Press:  20 November 2018

H. A. Eliopoulos
H. A. Eliopoulos*
Affiliation:
Assumption University of Windsor
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In a paper published in 1956, Rund (4) developed the differential geometry of a hypersurface of n— 1 dimensions imbedded in a Finsler space of n dimensions, considered as locally Minkowskian.

The purpose of the present paper is to provide an extension of the results of (4) and thus develop a theory for the case of m-dimensional subspaces imbedded in a generalized (Finsler) metric space.

We consider an n-dimensional differentiable manifold Xn and we restrict our attention to a suitably chosen co-ordinate neighbourhood of Xn in which a co-ordinate system xi (i= 1, 2, … , n), is defined. A system of equations of the type xi = xi(t) defines a curve C of Xn the tangent vector dxi/dt of which is denoted by xi.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 235 - 255
Copyright
Copyright © Canadian Mathematical Society 1959

References

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