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Projective invariant metrics for Einstein spaces

Published online by Cambridge University Press:  22 January 2016

Shoshichi Kobayashi
Shoshichi Kobayashi*
Affiliation:
Department of Mathematics, University of California, Berkeley and Mathematisches Institut der Universität Bonn
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In my recent paper [1], I associated a projectively invariant pseudo-distance dM to every affinely connected manifold M and proved the following

Theorem 1. Let M be a Riemannian manifold with metric and Ricci tensor RicM such that RicM ≤–c2. Let δM be the Riemannian distance defined by .

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 73 , March 1979 , pp. 171 - 174
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

References

[1] Kobayashi, S., Projective structures of hyperbolic type, Proc. U.S.-Japan Seminar on Minimal Submanifolds and Geodesies (1978).Google Scholar
[2] Kobayashi, S. and Sasaki, T., Projective structures with trivial intrinsic pseudo-distance, ibid.Google Scholar
[3] Nagano, T., The projective transformation on a space with parallel Ricci tensor, Kodai Math. Seminar Reports 11 (1959), 131–138.Google Scholar
[4] Tanaka, N., Projective connections and projective transformations, Nagoya Math. J. 12 (1957), 1–24.Google Scholar