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On Homotopic Harmonic Maps

Published online by Cambridge University Press:  20 November 2018

Philip Hartman
Philip Hartman*
Affiliation:
The Johns Hopkins University
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Let M, M′ be C∞ Riemann manifolds such that

(1.0) M is compact;

(1.1) M′ is complete and its sectional curvatures are non-positive.

In terms of local coordinates x = (x1, … , xn) on M and y = (y1, … , ym) on M′, let the respective Riemann elements of arc-length be

and Γijk, Γ′αβγ be the corresponding Christoffel symbols. When there is no danger of confusion, x (or y) will represent a point of M (or M′) or its coordinates in some local coordinate system.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 673 - 687
Copyright
Copyright © Canadian Mathematical Society 1967

References

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