Real hypersurfaces with parallel Ricci tensor of a complex space form
type: Item
instance of: scholarly article
title: Real hypersurfaces with parallel Ricci tensor of a complex space form
zbMATH Open document ID: 0678.53046
author: U-Hang Ki
published in: Tsukuba Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/2241/7222
review text: Let \(M\) be a real hypersurface of the complex space form \(M_n(c)\) such that the immersion induces on \(M\) a metric contact structure \((J,g,P)\). It is known that there does not exist such a hypersurface \(M\) of \(P_n\mathbb{C}\) with parallel Ricci tensor on which the structure vector field \(P\) is principal, and that there exists no Einstein hypersurface in \(H_n\mathbb{C}\). Now, one says that the Riemannian curvature tensor is harmonic if its Ricci tensor is of Codazzi type. Then it is also known that there does not exist \(M\) with harmonic curvature in \(M_n(c).\) In this paper the author tries to improve these scattered theorems, and presents the more uniformized theorems as follows. There does not exist any \(M\) with parallel Ricci tensor of \(M_n(c)\). Also, there exists no \(M\) with harmonic curvature of \(M_n(c)\) satisfying one of the following conditions: (1) \(P\) is an eigenvector corresponding to the Ricci tensor, (2) the number of Ricci curvatures does not exceed 2.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 4111505
zbMATH Keywords: metric contact structure
zbMATH Keywords: Ricci tensor
zbMATH Keywords: Codazzi type
zbMATH Keywords: harmonic curvature
reviewed by: Tanjiro Okubo
MaRDI profile type: Publication
OpenAlex ID: W1577496728
DOI: 10.21099/TKBJM/1496161007
description: scientific article; zbMATH DE number 4111505