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On Certain Mappings of Riemannian Manifolds

Published online by Cambridge University Press:  22 January 2016

Minoru Kurita
Minoru Kurita*
Affiliation:
Mathematical Institute, Nagoya University
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In this paper we consider certain tensors associated with differentiable mappings of Riemannian manifolds and apply the results to a p-mapping, which is a special case of a subprojective one in affinely connected manifolds (cf. [1], [7]). The p-mapping in Riemannian manifolds is a generalization of a conformal mapping and a projective one. From a point of view of differential geometry an analogy between these mappings is well known. On the other hand it is interesting that a stereographic projection of a sphere onto a plane is conformal, while a central projection is projectve, namely geodesic-preserving. This situation was clarified partly in [6]. A p-mapping defined in this paper gives a precise explanation of this and also affords a certain mapping in the euclidean space which includes a similar mapping and an inversion as special cases.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 25 , 1965 , pp. 121 - 142
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1965

References

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