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Umbilical submanifolds of $\mathbb{S}^n\times \mathbb{R}$
Umbilical submanifolds Differential Geometry
2011/8/30
Abstract: We give a complete classification of umbilical submanifolds of arbitrary dimension and codimension of $\Sf^n\times \R$, extending the classification of umbilical surfaces in $\Sf^2\times \R$...
Optimal Inequalities Characterising Quasi-umbilical Submanifolds
Chen curvature Casorati curvature quasi-umbilical
2010/1/22
A family of optimal inequalities is obtained involving the intrinsic scalar curvature and the extrinsic Casorati curvature of submanifolds of real space forms. Equality holds in the inequalities if a...