Maeda, Sadahiro On some isotropic submanifolds in spheres. (English) Zbl 1007.53045 Proc. Japan Acad., Ser. A 77, No. 10, 173-175 (2001). In a joint paper with P. Verheyen in Math. Ann. 269, 417-429 (1984; Zbl 0536.53053), B.-Y. Chen proved the following result: Let \(M^n\) be a connected compact isotropic submanifold of a sphere \(S^{n+p}\) of constant curvature \(\widetilde c\). If \(M^n\) has constant mean curvature \(H\), and if the sectional curvature function \(K\) of \(M^n\) satisfies \(K \geq (H^2+\widetilde c)/2\), then \(M^n\) is totally umbilical in \(S^{n+p}\). In the present paper the author constructs counterexamples to the above result. Reviewer: Jürgen Berndt (Hull) MSC: 53C40 Global submanifolds Keywords:isotropic submanifolds; constant mean curvature; sphere Citations:Zbl 0536.53053 PDF BibTeX XML Cite \textit{S. Maeda}, Proc. Japan Acad., Ser. A 77, No. 10, 173--175 (2001; Zbl 1007.53045) Full Text: DOI OpenURL References: [1] O’Neill, B.: Isotropic and Kaehler immesions. Canadian J. Math., 17 , 905-915 (1965). · Zbl 0171.20503 [2] Shen, Y. B.: On isotropic submanifolds with constant mean curvature. Chinese Ann. Math. Ser. A, 5 , 117-122 (1984) (in Chinese). · Zbl 0518.53056 [3] Takahashi, T.: Minimal immersions of Riemannian manifolds. J. Math. Soc. Japan, 18 , 380-385 (1966). · Zbl 0145.18601 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.