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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.
In this paper, we introduce the Mus-Sasaki metric on the tangent bundle as a new natural metric non-rigid on . First we investigate the geometry of the Mus-Sasakian metrics and we characterize the sectional curvature and the scalar curvature.
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