2019/10/07 by Ye‐Lin Ou, Ou, Ye-Lin · 1 citation
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.1910.02572
In this note, we generalize biharmonic equation for rotationally symmetric maps ([4], [16], [10]) to equivariant maps between model spaces and use it to give a complete classification of rotationally symmetric conformal biharmonic maps from a 4-dimensional space form into a 4-dimensional model space. We also give an improved second variation formula for biharmonic maps into a space form and use it to prove that there exists no stable proper biharmonic maps with constant square norm of tension field from a compact Riemannian manifold without boundary into a space form of positive sectional curvature.