A characterization of quadrics by the principal curvature functions
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- Dillen, F., Lusala, T., Scherfner, M. et al. Arch. Math. (2003) 81: 342. doi:10.1007/s00013-003-4735-8
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We consider the difference tensor field of the Levi-Civita connections of the first and third fundamental form for non-degenerate hypersurface immersions in space forms. Within this framework, we characterize quadrics in terms of their principal curvature functions.