Real hypersurfaces with harmonic Weyl tensor of a complex space form
type: Item
instance of: scholarly article
title: Real hypersurfaces with harmonic Weyl tensor of a complex space form
zbMATH Open document ID: 0716.53026
author: U-Hang Ki
author: Hisao Nakagawa
author: Young Jin Suh
published in: Hiroshima Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: The article is concerned with real hypersurfaces in a complex space form \(M_ n(c)\) of holomorphic sectional curvature \(c\neq 0\) and of dimension \(n\geq 3\), where the real hypersurfaces are assumed to satisfy certain (intrinsic) curvature conditions. The main result is a classification of all complete ``cyclic Ryan'' hypersurfaces of \(M_ n(c)\); its proof is based on the Cecil/Ryan and Montiel's classification of pseudo-Einstein hypersurfaces in \(M_ n(c)\). Moreover, the authors show that there are no real hypersurfaces with harmonic Weyl tensor in \(M_ n(c)\). This assertion generalizes results of Ki, Kim, Kon Kwon/Nakagawa and Montiel; see in particular \textit{H.-J. Kim} [Tsukuba J. Math. 12, No.2, 451-457 (1988; Zbl 0661.53013)] and \textit{J.-H. Kwon} and \textit{H. Nakagawa} [J. Aust. Math. Soc., Ser. A 47, No.1, 108-113 (1989; Zbl 0692.53005)] for the analogous result on hypersurfaces with harmonic curvature.
reviewed by: Helmut Reckziegel
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53B35
zbMATH DE Number: 4180241
zbMATH Keywords: cyclic Ryan hypersurfaces
zbMATH Keywords: real hypersurfaces
zbMATH Keywords: complex space form
zbMATH Keywords: harmonic Weyl tensor
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206454442
OpenAlex ID: W2131417890
Wikidata QID: Q128869212
DOI: 10.32917/HMJ/1206454442
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description: scientific article; zbMATH DE number 4180241