We give necessary and sufficient conditions for Riemannian maps to be biharmonic. We also define pseudo-umbilical Riemannian maps as a generalization of pseudo-umbilical submanifolds and show that such Riemannian maps put some restrictions on the target manifolds.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-1-4, author = {Bayram Sahin}, title = {Biharmonic Riemannian maps}, journal = {Annales Polonici Mathematici}, volume = {101}, year = {2011}, pages = {39-49}, zbl = {1226.53064}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-1-4} }
Bayram Ṣahin. Biharmonic Riemannian maps. Annales Polonici Mathematici, Tome 101 (2011) pp. 39-49. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-1-4/