Almost complex structure in the frame bundle of an almost contact metric manifold
type: Item
instance of: scholarly article
title: Almost complex structure in the frame bundle of an almost contact metric manifold
zbMATH Open document ID: 0585.53028
DOI: 10.1007/BF01229810
author: B. George
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173798
review text: On the frame bundle \({\mathcal F}(M)\) of an almost contact metric manifold (M,\(\phi\),\(\xi\),\(\eta\),g), we define an almost complex structure J and obtain that (\({\mathcal F}(M),g^ D,J)\) is an almost Hermitian manifold, where \(g^ D\) is the Sasaki-Mok metric induced on \({\mathcal F}(M)\). The integrability of the almost complex structure J and its relationship with the normality of the almost contact structure on M is studied. Moreover, we prove that (\({\mathcal F}(M),g^ D,J)\) cannot be either an almost Kähler or a nearly Kähler manifold unless it is a Kähler manifold.
Mathematics Subject Classification ID: 53B35
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 3937984
zbMATH Keywords: frame bundle
zbMATH Keywords: almost complex structure
zbMATH Keywords: almost Hermitian manifold
zbMATH Keywords: almost contact structure
zbMATH Keywords: Kähler manifold
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3937984