2024/10/27 by Ze-Ping Wang, Wang, Ze-Ping, Qin, Li-Hua +2
Mathematics · #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2410.20517
We first study f-biharmonicity of totally umbilical hypersurfaces in a generic Riemannian manifold and then prove that any totally umbilical proper f-biharmonic hypersurface in a nonpositively curved manifold has to be noncompact. We also explore f-biharmonicity of totally umbilical hyperplanes in a conformally flat space. Secondly, we construct f-biharmonic surfaces and biharmonic conformal immersions of the associated surfaces into a conformall flat 3-space and also give a complete classification of f-biharmonic surfaces of nonzero constant mean curvature in 3-space forms. Finally, we especially investigate f-biharmonicity of hypersurfaces into a conformally flat space of negative sectional curvature. We show that any totally umbilical f-biharmonic surface of a 3-manifold with nonpositve sectional curvature is minimal whilst there are proper f-biharmonic m-dimensional submanifolds with m≥3 and m≠4 into nonpositvely curved manifolds.