[Hypersurfaces réelles conformément plates dans les plans complexes non plats]
Dans cette note, nous démontrons qu'il n'existe pas d'hypersurface réelle conformément plate dans les espaces de formes complexes de dimension deux, non plats, pourvu que le champ de vecteurs structurel soit champ de vecteur propre de l'opérateur de Ricci. Ceci étend des résultats récents de Cho (Conformally flat normal almost contact 3-manifolds, Honam Math. J. 38 (2016) 59–69) et Kron (3-dimensional real hypersurfaces with η-harmonic curvature, in : Hermitian–Grassmannian Submanifolds, Springer, Singapore, 2017, pp. 155–164).
In this paper, we prove that there are no conformally flat real hypersurfaces in nonflat complex space forms of complex dimension two provided that the structure vector field is an eigenvector field of the Ricci operator. This extends some recent results by Cho (Conformally flat normal almost contact 3-manifolds, Honam Math. J. 38 (2016) 59–69) and Kon (3-dimensional real hypersurfaces with η-harmonic curvature, in: Hermitian–Grassmannian Submanifolds, Springer, Singapore, 2017, pp. 155–164).
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@article{CRMATH_2018__356_7_823_0,
author = {Wang, Yaning},
title = {Conformally flat real hypersurfaces in nonflat complex planes},
journal = {Comptes Rendus. Math\'ematique},
pages = {823--829},
publisher = {Elsevier},
volume = {356},
number = {7},
year = {2018},
doi = {10.1016/j.crma.2018.04.025},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2018.04.025/}
}
TY - JOUR AU - Wang, Yaning TI - Conformally flat real hypersurfaces in nonflat complex planes JO - Comptes Rendus. Mathématique PY - 2018 SP - 823 EP - 829 VL - 356 IS - 7 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2018.04.025/ DO - 10.1016/j.crma.2018.04.025 LA - en ID - CRMATH_2018__356_7_823_0 ER -
%0 Journal Article %A Wang, Yaning %T Conformally flat real hypersurfaces in nonflat complex planes %J Comptes Rendus. Mathématique %D 2018 %P 823-829 %V 356 %N 7 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2018.04.025/ %R 10.1016/j.crma.2018.04.025 %G en %F CRMATH_2018__356_7_823_0
Wang, Yaning. Conformally flat real hypersurfaces in nonflat complex planes. Comptes Rendus. Mathématique, Tome 356 (2018) no. 7, pp. 823-829. doi : 10.1016/j.crma.2018.04.025. http://archive.numdam.org/articles/10.1016/j.crma.2018.04.025/
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