General Mathematics, Vol. 5, No. 1 - 4, pp. 401-408, 1995
Abstract: The exterior parallelism of immersions in the sense of H.R.\ Farran and S.A.\ Robertson [J.\ London Math.\ Soc.\ (2) {\bf 35} (1987), 527--538] is studied in the case of ambient spaces of constant curvature. The different types of parallel ranks are generalized to this situation. Their local version is shown to be closely related with the curvature structure of certain subbundles of the normal bundle. It also has particular implications on the locus for the focal points of an immersion. Finally it is shown that the local parallel rank is preserved if the image of the immersion is subject to a local conformal transformation into possibly another ambient space of constant curvature.
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