Lee, Ji-Eun Pseudo-Hermitian 2-type Legendre surfaces in the unit sphere \(S^5\). (English) Zbl 1452.53016 Commun. Korean Math. Soc. 35, No. 1, 251-260 (2020). Summary: In this paper, we show that it is Chen surfaces that non-minimal pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in \(S^5\). Moreover, we show that pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in \(S^5\) are locally the product of two pseudo-Hermitian circles. MSC: 53B25 Local submanifolds 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) Keywords:Legendre surface; Sasakian space forms; pseudo-Hermitian structure; \(k\)-type submanifold; mass-symmetric PDFBibTeX XMLCite \textit{J.-E. Lee}, Commun. Korean Math. Soc. 35, No. 1, 251--260 (2020; Zbl 1452.53016) Full Text: DOI References: [1] C. Baikoussis and D. E. Blair, 2-type integral surfaces in S5(1), Tokyo J. Math. 14 (1991), no. 2, 345-356. https://doi.org/10.3836/tjm/1270130378 · Zbl 0763.53055 · doi:10.3836/tjm/1270130378 [2] D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, 203, Birkhauser Boston, Inc., Boston, MA, 2002. https://doi.org/10.1007/978-1-4757-3604-5 · Zbl 1011.53001 [3] B.-Y. Chen, Total mean curvature and submanifolds of finite type, Series in Pure Mathematics, 1, World Scientific Publishing Co., Singapore, 1984. https://doi.org/10.1142/0065 · Zbl 0537.53049 [4] J. T. Cho, Geometry of contact strongly pseudo-convex CR-manifolds, J. Korean Math. Soc. 43 (2006), no. 5, 1019-1045. https://doi.org/10.4134/JKMS.2006.43.5.1019 · Zbl 1119.53050 · doi:10.4134/JKMS.2006.43.5.1019 [5] J.-E. Lee, Laplacians and Legendre surfaces in pseudo-Hermitian geometry, Bull. Iranian Math. Soc. 44 (2018), no. 4, 899-913. https://doi.org/10.1007/s41980-018-0058-1 · Zbl 1426.53029 · doi:10.1007/s41980-018-0058-1 [6] N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan. J. Math. (N.S.) 2 (1976), no. 1, 131-190. https://doi.org/10.4099/math1924.2.131 · Zbl 0346.32010 · doi:10.4099/math1924.2.131 [7] S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 (1989), no. 1, 349-379. https://doi.org/10.2307/2001446 · Zbl 0677.53043 · doi:10.1090/S0002-9947-1989-1000553-9 [8] S. · Zbl 0379.53016 · doi:10.4310/jdg/1214434345 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.