A generalization of the Goldberg conjecture for coKähler manifolds
type: Item
instance of: scholarly article
title: A generalization of the Goldberg conjecture for coKähler manifolds
zbMATH Open document ID: 1392.53086
author: Yaning Wang
published in: Mediterranean Journal of Mathematics
publication date: 2016-12-07T00:00:00Z
review text: A celebrated conjecture in Kähler geometry is the Goldberg conjecture: any compact Einstein almost Kähler manifold is Kähler. The best result for proving Goldberg's conjecture was obtained by Sekigawa who proved that any compact Einstein almost Kähler manifold with non-negative scalar curvature is Kähler. Since Sasakian manifolds are the odd-dimensional analogues of Kähler manifolds, \textit{C. P. Boyer} and \textit{K. Galicki} [Proc. Am. Math. Soc. 129, No. 8, 2419--2430 (2001; Zbl 0981.53027)] first considered Goldberg's conjecture in the framework of contact metric geometry and proved that any compact Einstein K-contact manifold is Sasakian. However, co-Kähler manifolds can also be considered as the odd-dimensional version of Kähler manifolds. The aim of the paper under review is just to study the existence of a Goldberg-like conjecture in the framework of co-Kähler geometry.
reviewed by: Manuel de León
Mathematics Subject Classification ID: 53D15
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 6661796
zbMATH Keywords: Ricci soliton
zbMATH Keywords: gradient Ricci soliton
zbMATH Keywords: (almost) co-Kähler manifold
zbMATH Keywords: \((\kappa, \mu)\)-nullity condition
Wikidata QID: Q122960653
MaRDI profile type: Publication
full work available at URL: s00009-015-0646-8
OpenAlex ID: W2183070800
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DOI: 10.1007/S00009-015-0646-8
description: scientific article; zbMATH DE number 6661796