Address.
School of Mathematics and Statistics,
Central China Normal University,
Wuhan,430079, P. R. China
E-mail. zrzhou@ccnu.edu.cn , qunchen@mail.ccnu.edu.cn
Abstract.
In this article, we obtain a gap property of energy densities of
harmonic maps from a closed Riemannian manifold to a Grassmannian
and then, use it to Gaussian maps of some submanifolds to get a
gap property of the second fundamental forms.
AMSclassification. 58E20, 53C43.
Keywords. Grassmannian, Gaussian map, mean curvature, the second fundamental form.