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- W2963742356 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." @default.
- W2963742356 created "2019-07-30" @default.
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- W2963742356 date "2017-01-01" @default.
- W2963742356 modified "2023-09-26" @default.
- W2963742356 title "Almost conformally flat hypersurfaces" @default.
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- W2963742356 doi "https://doi.org/10.1215/ijm/1520046208" @default.
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