Kodai Mathematical Journal
Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991
On C-totally real submanifolds of $\mathbb{S}^{2n+1}(1)$ with non-negative sectional curvature
Xiuxiu ChengZejun Hu
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2023 年 46 巻 2 号 p. 184-206

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For all n ≥ 4, we give a complete classification of the compact n-dimensional minimal C-totally real submanifolds in the (2n + 1)-dimensional unit sphere with non-negative sectional curvature. This generalizes the results of Yamaguchi et al (Proc Amer Math Soc 54: 276-280, 1976) for n = 2 and, Dillen and Vrancken (Math J Okayama Univ 31: 227-242, 1989) for n = 3. Additionally, we show that, as compact minimal C-totally real submanifolds, the standard embeddings of the symmetric spaces SU(m)/SO(m), SU(m), SU(2m)/Sp(m) for each m ≥ 3, and E6/F4 into are all Willmore submanifolds, with n = 1/2m(m - 1) - 1, m2 - 1, 2m2 - m - 1 and 26, respectively.

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© 2023 Department of Mathematics, Tokyo Institute of Technology
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