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Topological obstructions for submanifolds in low codimension

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Abstract

We prove integral curvature bounds in terms of the Betti numbers for compact submanifolds of the Euclidean space with low codimension. As an application, we obtain topological obstructions for \(\delta \)-pinched immersions. Furthermore, we obtain intrinsic obstructions for minimal submanifolds in spheres with pinched second fundamental form.

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Notes

  1. The mean curvature is given by \(H=\Vert {\mathcal {H}}\Vert \), where \({\mathcal {H}}\) denotes the mean curvature vector field.

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Authors and Affiliations

  1. Department of Mathematics, University of Ioannina, 45110, Ioannina, Greece

    Christos-Raent Onti & Theodoros Vlachos

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  1. Christos-Raent Onti
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  2. Theodoros Vlachos
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Correspondence to Theodoros Vlachos.

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Onti, CR., Vlachos, T. Topological obstructions for submanifolds in low codimension. Geom Dedicata 196, 11–26 (2018). https://doi.org/10.1007/s10711-017-0301-6

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