155 research outputs found
Biharmonic submanifolds with parallel mean curvature vector field in spheres
We present some results on the boundedness of the mean curvature of proper
biharmonic submanifolds in spheres. A partial classification result for proper
biharmonic submanifolds with parallel mean curvature vector field in spheres is
obtained. Then, we completely classify the proper biharmonic submanifolds in
spheres with parallel mean curvature vector field and parallel Weingarten
operator associated to the mean curvature vector field.Comment: 15 pages. Minor changes made and one section adde
Explicit Formulas for Non-Geodesic Biharmonic Curves of the Heisenberg Group
We consider the biharmonicity condition for maps between Riemannian manifolds
(see [BK]), and study the non-geodesic biharmonic curves in the Heisenberg
group H_3. First we prove that all of them are helices, and then we obtain
explicitly their parametric equations.Comment: 16 pages, 2 figure
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