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Symmetry properties of S-space-forms

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Abstract

In this paper, we study the pseudo-symmetry type of the \({(2n+s)}\) -dimensional S-space-forms with f-sectional curvature c, which generalize the Sasakian-space-forms. We prove that an S-space-form, with \({s\geq2}\) and \({n\geq1}\) can not be Ricci-pseudo-symmetric, thus, not pseudo-symmetric. We also show that, for \({s\geq2}\) and \({n\geq1}\) or s = 1 and \({n\geq2,}\) the \({(2n+s)}\) -dimensional S-space-form can not be Ricci-generalized pseudo-symmetric.

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Correspondence to Rachida Kaid.

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This study was PNR-DGRSDT Project (Grant No. 8/U29/690).

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Kaid, R., Belkhelfa, M. Symmetry properties of S-space-forms. J. Geom. 106, 513–530 (2015). https://doi.org/10.1007/s00022-015-0262-6

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  • DOI: https://doi.org/10.1007/s00022-015-0262-6

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