Conformally Flat Normal Almost Contact 3-Manifolds

Abstract

Abstract. We classify conformally flat Kenmotsu 3-manifolds and classify conformally flat cosympletic 3-manifolds.

Conformally flat real hypersurfaces in nonflat complex planes

“…A real hypersurface in a nonflat complex space form is said to be totally η-umbilical if the shape operator is given by A = aid + bη ⊗ ξ for some constants a, b and id denotes the identity transformation. Cho in [3,Proposition 5.6] proved that a totally η-umbilical real hypersurface in a nonflat complex space form of complex dimension two does not admit conformally flat structure. Our Theorem 1.4 is an extension of the above result because the total η-umbilication of the shape operator A implies that ξ is an eigenvector field of the Ricci operator.…”