Classification of hypersurfaces with two distinct principal curvatures and closed Möbius form in $$\mathbb{S}^{m + 1}$$

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Let x be an m-dimensional umbilic-free hypersurface in an (m + 1)-dimensional unit sphere \(\mathbb{S}^{m + 1}\) (m ⩾ 3). In this paper, we classify and explicitly express the hypersurfaces with two distinct principal curvatures and closed Mobius form, and then we characterize and classify conformally flat hypersurfaces of dimension larger than 3.