Yamaguchi, Seiichi; Nemoto, Hiroaki; Kawabata, Nobuyuki Extrinsic spheres in a Kähler manifold. (English) Zbl 0578.53038 Mich. Math. J. 31, 15-19 (1984). In [ibid. 23(1976), 327-330 (1977; Zbl 0349.53040)], the reviewer proved that a complete, connected, simply-connected, even-dimensional extrinsic sphere of a Kähler manifold is isometric to an ordinary sphere if its normal connection is flat. In the present paper, the authors generalize the reviewer’s result by omitting the condition of a flat normal connection to obtain the following result. Theorem. A complete, connected, simply-connected extrinsic sphere \(M^ n\) in a Kähler manifold is one of the following: (1) an ordinary sphere, (2) \(M^ n\) is homothetic to a Sasakian manifold, or (3) \(M^ n\) is a totally real submanifold with non-parallel f-structure in the normal bundle. Reviewer: B.Y.Chen Cited in 1 ReviewCited in 4 Documents MSC: 53C40 Global submanifolds Keywords:extrinsic sphere; Kähler manifold; Sasakian manifold; totally real submanifold; f-structure Citations:Zbl 0349.53040 PDF BibTeX XML Cite \textit{S. Yamaguchi} et al., Mich. Math. J. 31, 15--19 (1984; Zbl 0578.53038) Full Text: DOI OpenURL