80 research outputs found
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
Classification results for biharmonic submanifolds in spheres
We classify biharmonic submanifolds with certain geometric properties in
Euclidean spheres. For codimension 1, we determine the biharmonic hypersurfaces
with at most two distinct principal curvatures and the conformally flat
biharmonic hypersurfaces. We obtain some rigidity results for pseudo-umbilical
biharmonic submanifolds of codimension 2 and for biharmonic surfaces with
parallel mean curvature vector field. We also study the type, in the sense of
B-Y. Chen, of compact proper biharmonic submanifolds with constant mean
curvature in spheres.Comment: Dedicated to Professor Vasile Oproiu on his 65th birthday, 14 page
Properties of biharmonic submanifolds in spheres
In the present paper we survey the most recent classification results for
proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some
new results concerning geometric properties of proper biharmonic constant mean
curvature submanifolds in spheres.Comment: 10 pages; contribution to the Proceedings of the 11-th International
Conference on Geometry, Integrability and Quantization, Varna 2009, Bulgari
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