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We characterize helix surfaces in the Berger sphere. In particular, we prove that, locally, a helix surface is invariant by the action of a 1-parameter group of isometries of the ambient space.
Deforming submanifolds of arbitrary codimension in a sphere
Mean curvature flow submanifolds of spheres convergence theorem differentiable sphere theorem integral curvature
2012/4/17
In this paper, we prove some convergence theorems for the mean curvature flow of closed submanifolds in the unit sphere $\mathbb{S}^{n+d}$ under integral curvature conditions. As a consequence, we obt...
Curvatures of weighted metrics on tangent sphere bundles
metric connection tangent sphere bundle curvature
2011/9/21
Abstract: We determine the curvature equations of natural metrics on tangent bundles and radius r tangent sphere bundles S_rM of a Riemannian manifold M. A family of positive scalar curvature metrics ...
Curvature properties of pseudo-sphere bundles over paraquaternionic manifolds
twistor space Einstein manifold paraquaternionic structure mixed 3-structure
2011/9/21
Abstract: In this paper we obtain several curvature properties of the twistor and reflector spaces of a paraquaternionic K\"{a}hler manifold and prove the existence of both positive and negative mixed...