Urakawa, Hajime Geometry of harmonic maps and biharmonic maps. (English) Zbl 1325.53003 Barletta, Elisabetta (ed.), Lecture notes of Seminario Interdisciplinare di Matematica. Vol. XI. Potenza: Seminario Interdisciplinare di Matematica (S.I.M.) (ISBN 978-88-97478-03-4/pbk). Lecture Notes of Seminario Interdisciplinare di Matematica 11, 41-83 (2014). Summary: A biharmonic map is a critical point of the bienergy in the space of \(C^\infty\) maps between two Riemannian manifolds, and it is a natural extension of a harmonic map which is a critical point of the energy. In this paper, we give a brief survey on our recent works for biharmonic maps.For the entire collection see [Zbl 1294.00024]. MSC: 53-02 Research exposition (monographs, survey articles) pertaining to differential geometry 53C43 Differential geometric aspects of harmonic maps Keywords:bubbling phenomena; biharmonic Lagrangian submanifolds; \(k\)-harmonic maps; triharmonic immersion PDFBibTeX XMLCite \textit{H. Urakawa}, Lect. Notes Semin. Interdiscip. Mat. 11, 41--83 (2014; Zbl 1325.53003)