Remarks on some almost Hermitian structure on the tangent bundle. II
type: Item
instance of: scholarly article
title: Remarks on some almost Hermitian structure on the tangent bundle. II
zbMATH Open document ID: 1306.53019
author: Takashi Oguro
author: Yoshitsugu Takashima
published in: Nihonkai Mathematical Journal
publication date: 2014-10-24T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.nihmj/1413555410
reviewed by: Neda Bokan
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C56
zbMATH DE Number: 6361359
zbMATH Keywords: almost Hermitian manifold
zbMATH Keywords: almost hyper-complex structure
zbMATH Keywords: Kähler form
MaRDI profile type: Publication
cites work: On the Geometry of the Tangent Bundle.
cites work: The sixteen classes of almost Hermitian manifolds and their linear invariants
cites work: Remarks on some almost Hermitian structure on the tangent bundle
cites work: Q4516960
cites work: Q4383968
review text: Let \(M\) and \(TM\) be an almost Hermitian manifold and its tangent bundle respectively. \textit{M. Tahara} et al. [Note Mat. 18, No. 1, 131--141 (1998; Zbl 0964.53021)] constructed three almost complex structures \(J_1,J_2,J_3\) on \(TM\), which define in special cases an almost hyper-complex structure. They also found a Riemannian metric \(G_1\) such that \((J_1,G_1)\) is an almost Hermitian structure on \(TM\). NEWLINENEWLINENEWLINEHere, the authors construct Riemannian metrics \(G_2\) and \(G_3\) on \(TM\) such that \((J_2,G_2)\) and \((J_3,G_3)\) are almost Hermitian structures on \(TM\). For these structures \((J_i,G_i)\), \(i=1,2,3\), they find conditions such that \((TM,J_i,G_i)\) belongs to the classes constructed by \textit{A. Gray} and \textit{L. M. Hervella} [Ann. Mat. Pura Appl. (4) 123, 35--58 (1980; Zbl 0444.53032)].
description: scientific article; zbMATH DE number 6361359