Kaimakamis and Panagiotidou in [Taiwanese J. Math. 18(6) (2014), 1991–1998] proposed an open question: are there real hypersurfaces in nonflat complex space forms whose ∗-Ricci tensor satisfies the condition of 𝔻-parallelism? In this short note, we present an affirmative answer and prove that a three-dimensional real hypersurface in a nonflat complex space form has 𝔻-parallel ∗-Ricci tensor if and only if it is locally congruent to either a geodesic hypersphere of radius r in ℂ H2(c) with or a ruled real hypersurface.
Ivey, T.—Ryan, P. J.: The ∗-Ricci tensor for hypersurfaces in ℂ Pn and ℂ Hn, Tokyo J. Math. 34 (2011), 445–471.
Kaimakamis, G.—Panagiotidou, K.: The ∗-Ricci tensor of real hypersurfaces in symmetric spaces of rank one or two. In: Real and Complex Submanifolds, Springer Proceedings in Mathematics & Statistics, New York, 2014.
Kaimakamis, G.—Panagiotidou, K.: Parallel ∗-Ricci tensor of real hypersurfaces in ℂ P2 and ℂ H2, Taiwanese J. Math. 18 (2014), 1991–1998.
Kaimakamis, G.—Panagiotidou, K.: Conditions of parallelism of ∗-Ricci tensor of three dimensional real hypersurfaces in non-flat complex space forms, Taiwanese J. Math. 21 (2017), 305–318.10.11650/tjm/7814)| false
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