Abstract
For submanifolds of general dimension and codimension in statistical manifolds of constant curvature, a sharp inequality of Wintgen type is given by us. It generalizes the inequality (1) obtained for statistical surfaces of codimension 2 in Aydin and Mihai (Math Inequal Appl 22:115–128, 2019) and turns out to be stronger than the generalized Wintgen inequality (2) proved in Aydin et al. (Bull Math Sci 7:155–166, 2017). Statistical submanifolds attaining the equality everywhere are also investigated in this paper. In the case of codimension 2, we generalize a characterization theorem of Wintgen ideal submanifolds in Riemannian space forms, which said that for those non-minimal ones, having constant mean curvature implies being totally umbilical.
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This work is supported by Yueqi Young Scholar project of CUMTB and NSFC No. 12171473.
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Wan, J., Xie, Z. Wintgen inequality for statistical submanifolds in statistical manifolds of constant curvature. Annali di Matematica 202, 1369–1380 (2023). https://doi.org/10.1007/s10231-022-01284-w
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DOI: https://doi.org/10.1007/s10231-022-01284-w