Abstract
We generalize biharmonic maps between Riemannian manifolds into the case of the domain being V‐manifolds. We obtain the first and second variations of biharmonic maps on V‐manifolds. Since a biharmonic map from a compact V‐manifold into a Riemannian manifold of nonpositive curvature is harmonic, we construct a biharmonic non‐harmonic map into a sphere. We also show that under certain condition the biharmonic property of f implies the harmonic property of f. We finally discuss the composition of biharmonic maps on V‐manifolds.
Highlights
Following Eells, Sampson, and Lemaire’s tentative ideas [7, 8, 9], Jiang first discussed biharmonic maps between Riemannian manifolds in his two articles [10, 11] in China in 1986, which gives the conditions for biharmonic maps
Biharmonic maps are the extensions of harmonic maps, and their study provides a source in partial differential equations, differential geometry, and analysis
We show that a biharmonic map from a compact V-manifold into a Riemannian manifold of nonpositive curvature is a harmonic map in Theorem 2.4
Summary
Following Eells, Sampson, and Lemaire’s tentative ideas [7, 8, 9], Jiang first discussed biharmonic (or 2-harmonic) maps between Riemannian manifolds in his two articles [10, 11] in China in 1986, which gives the conditions for biharmonic maps. A biharmonic map f : M → N between Riemannian manifolds is the smooth critical point of the bi-energy functional
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