Gap properties of harmonic maps and submanifolds

Qun Chen, Zhen-Rong Zhou

School of Mathematics and Statistics, Central China Normal University, Wuhan,430079, P. R. China

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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.