614 research outputs found
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
A short survey on biharmonic maps between Riemannian manifolds
In this short survey we report on the theory of biharmonic maps between
Riemannian manifolds.Comment: 20 page
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