𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms

Yaning Wang 1
  • 1 School of Mathematics and Information Science, Henan Normal University, 453007, Henan, Xinxiang, P. R. China
Yaning Wang
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  • School of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, Henan, P. R. China
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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 or a ruled real hypersurface.

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    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.

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    Tachibana, S.: On almost-analytic vectors in almost Kählerian manifolds, Tohoku Math. J. 11 (1959), 247–265.

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Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process.

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