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In this paper we study the minimal norm tensors for general third covariant tensors and fourth covariant tensors, using this we can give a new explanation of Weyl tensor and Cotten tensor: Weyl tensor is the minimal norm tensor of Riemannian curvature tensor and Cotten tensor is the minimal norm tensor of divergence of Riemannian curvature tensor, and we also get some useful inequalities by computation the norm of minimal norm tensors.

In this paper, we consider the scalar curvature of a selfshrinker and get the gap theorem of the scalar curvature. We get also a relationship between the upper bound of the square of the length of the second fundamental form and the Ricci mean value.

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