Affiliation:
1. Department of Mathematics, Mascara University, Mascara 29000, Algeria
Abstract
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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Physics and Astronomy (miscellaneous)
Cited by
5 articles.
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