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𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms
Mathematica Slovaca ( IF 0.9 ) Pub Date : 2020-08-26 , DOI: 10.1515/ms-2017-0402 Yaning Wang 1
Mathematica Slovaca ( IF 0.9 ) Pub Date : 2020-08-26 , DOI: 10.1515/ms-2017-0402 Yaning Wang 1
Affiliation
Abstract 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 $\begin{array}{} \displaystyle \tanh(\frac{\sqrt{|c|}}{2}r) = \frac{1}{2} \end{array}$ or a ruled real hypersurface.
更新日期：2020-08-26
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