Some results on harmonic and bi-harmonic maps
2017 ◽
Vol 14
(07)
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pp. 1750098
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Keyword(s):
In this paper, we prove that any bi-harmonic map from a compact orientable Riemannian manifold without boundary [Formula: see text] to Riemannian manifold [Formula: see text] is necessarily constant with [Formula: see text] admitting a strongly convex function [Formula: see text] such that [Formula: see text] is a Jacobi-type vector field (or [Formula: see text] admitting a proper homothetic vector field). We also prove that every harmonic map from a complete Riemannian manifold into a Riemannian manifold admitting a proper homothetic vector field, satisfying some condition, is constant. We present an open problem.
1994 ◽
Vol 36
(1)
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pp. 77-80
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1986 ◽
Vol 29
(3)
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pp. 308-313
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2000 ◽
Vol 68
(2)
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pp. 145-154
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Keyword(s):
2005 ◽
Vol 16
(09)
◽
pp. 1017-1031
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2012 ◽
Vol 23
(09)
◽
pp. 1250095
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Keyword(s):