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arXiv · 0807.1836

Biharmonic maps between doubly warped product manifolds

Selcen Yüksel Perktaş·Erol Kılıç
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Abstract

In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds $B$ and $F$ into the doubly warped product $_{f}B\times_{b}F$ can not be proper biharmonic maps. Also we analyze the conditions for the biharmonicity of projections $_{f}B\times_{b}F\to B$ and $_{f}B\times_{b}F\to F$, respectively. Some characterizations for non-harmonic biharmonic maps are given by using product of harmonic maps and warping metric. Specially, in the case of $f=1$, the results for warped product in \cite{Balmus-mont} are obtained.

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Selcen Yüksel Perktaş, Erol Kılıç. 2008-08-01. Biharmonic maps between doubly warped product manifolds. https://arxiv.org/abs/0807.1836

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