Abstract
We prove a universal lower bound for the $L^{n/2}$-norm of the Weyl tensor in terms of the Betti numbers for compact $n$-dimensional Riemannian manifolds that are conformally immersed as hypersurfaces in the Euclidean space. As a consequence, we determine the homology of almost conformally flat hypersurfaces. Furthermore, we provide a necessary condition for a compact Riemannian manifold to admit an isometric minimal immersion as a hypersurface in the round sphere and extend a result due to Shiohama and Xu (J. Geom. Anal. 7 (1997) 377–386) for compact hypersurfaces in any space form.
Citation
Christos-Raent Onti. Theodoros Vlachos. "Almost conformally flat hypersurfaces." Illinois J. Math. 61 (1-2) 37 - 51, Spring and Summer 2017. https://doi.org/10.1215/ijm/1520046208
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