Mathematica Slovaca ( IF 0.654 ) Pub Date : 2020-07-24 , DOI: 10.1515/ms-2017-0402
Yaning Wang

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 $tanh⁡(|c|2r)=12$ or a ruled real hypersurface.

Kaimakamis和Panagiotidou在[Taiwanese J. Math。18（6）（2014），1991–1998]提出了一个开放的问题：非平面复杂空间形式中的真实超曲面的＊ -Ricci张量满足𝔻-平行度的条件吗？在这个简短的注释中，我们给出一个肯定的答案，并证明当且仅当它与半径为r的测地超球面局部一致时，非平面复杂空间形式的三维实超曲面才具有𝔻-平行∗ -Ricci张量。 ℂ ħ 2C ^）与$谭⁡（|C|2[R）=1个2$ 或规则的实际超曲面。

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