Biharmonic submanifolds in nonpositive space forms
Yu Fu, Min-chun Hong, Dan Yang
Abstract
We prove that there are no proper biharmonic submanifolds with parallel normalized mean curvature vector field in a nonpositive space form, in arbitrary dimension and codimension. We also prove that every biharmonic surface with flat normal bundle in a four-dimensional nonpositive space form is minimal. These results provide substantial support for Chen's conjecture and the generalized Chen's conjecture for hyperbolic space in higher codimensions.
Create a lesson
Related papers
A note on the BRST-BV Formalism Explanation of Deformation Quantization and Algebraic Index Theorem
Lihao Zhao
Conjugate radius and parabolicity along the Ricci flow
Chandan Kumar Mondal
Pure Spinor Factorization of Belinski-Zakharov Solitons and Regular Gravitational Instantons
Steffen Aksteiner
Flexibility of Laplace-Beltrami eigenfunctions under metric variation
Andrei Agrachev, Nicola Da Ponte, Antonio Lerario et al.
C1-rigidity of Hp,q-convex cocompact representations of Gromov hyperbolic groups
Nikolay Bogachev
A proof of the spectral rigidity for complex projective space
Kefeng Liu, Hao Xu