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On Preserving the Kobayashi Pseudodistance

Published online by Cambridge University Press:  22 January 2016

L. Andrew Campbell  and
Roy H. Ogawa
L. Andrew Campbell
Affiliation:
Department of Mathematics, University of California
Roy H. Ogawa
Affiliation:
Department of Mathematics, University of California
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If X is a complex space, the Kobayashi pseudo-distance dx is an intrinsic pseudometric on X defined as follows. If p and q are points of X, a chain α from p to q consists of intermediate points p0, …, pr with p0 = p and pr = q together with maps fi of the unit disc D = {z ∈ Cl‖z| < 1} into X and points ai and bi in D such that fi(ai) = Pi−1 and fi(bi) = pi for i = 1, …, r.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 57 , June 1975 , pp. 37 - 47
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

[1] Barth, Theodore J, “The Kobayashi Distance Induces the Standard Topology.” Proc. AMS 35 No. 2 (1972), 439–442.Google Scholar
[2] Gunning, Robert C. and Rossi, Hugo, “Analytic Functions of Several Complex Variables.” 1965. Prentice-Hall, Inc. Englewood Cliffs, N.J. Google Scholar
[3] Kaup, Wilhelm, “Infinitesimale Transformationsgruppen komplexer Räume.” Math. Annalen 160 (1965), 72–92.Google Scholar
[4] Kobayashi, Shoshichi, “Hyperbolic Manifolds and Holomorphic Mappings.” 1970. Marcel Dekker, Inc. New York.Google Scholar
[5] Rossi, Hugo, “Vector Fields on Analytic Spaces.” Annals of Math. 78 No. 3 (1963), 455–467.Google Scholar