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Gap properties of harmonic maps and submanifolds

Qun Chen, Zhen Rong Zhou (2005)

Archivum Mathematicum

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.

Geometry of Mus-Sasaki metric

Abderrahim Zagane, Mustapha Djaa (2018)

Communications in Mathematics

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

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