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The contact Whitney sphere


Abstract


In this paper, we introduce the contact Whitney sphere as an imbedding of the n--dimensional unit sphere as an integral submanifold of the standard contact structure on \R^{2n+1}. We obtain a general inequality for integral submanifolds in \R^{2n+1}, involving both the scalar curvature and the mean curvature, and we use the equality case in order to characterize the contact Whitney sphere. We also study a similar problem foranti-invariant submanifolds of \R^{2n+1}, tangent to the structure vector field.


DOI Code: 10.1285/i15900932v20n2p125

Keywords: Integral submanifolds; Whitney spheres; Scalar curvature; Mean curvature

Classification: 53C15; 53C40; 53D10

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