The local structure of trans-Sasakian manifolds
type: Item
instance of: scholarly article
title: The local structure of trans-Sasakian manifolds
zbMATH Open document ID: 0772.53036
DOI: 10.1007/BF01760000
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1993-05-16T00:00:00Z
review text: A trans-Sasakian structure is, in some sense, an analogue of a locally conformal Kähler structure on an almost Hermitian manifold. Two remarkable subclasses of trans-Sasakian structures are those called \({\mathcal C}_ 5\)- and \({\mathcal C}_ 6\)-structures, which contain the Kenmotsu and Sasakian structures respectively. In this paper the author has completely characterized the local nature of trans-Sasakian structures on differentiable manifolds of dimension \(\geq 5\). This has been done through two stages: 1) characterizing the local nature of \({\mathcal C}_ 5\)- and \({\mathcal C}_ 6\)-structures; 2) showing that a trans- Sasakian structure is either of class \({\mathcal C}_ 5\) or of class \({\mathcal C}_ 6\). The author has finally obtained some examples of 3-dimensional trans-Sasakian manifolds which are neither of class \({\mathcal C}_ 5\) nor of class \({\mathcal C}_ 6\).
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 169832
zbMATH Keywords: Kenmotsu structure
zbMATH Keywords: conformal Kähler structure
author: Juan Carlos Marrero
reviewed by: Nabil L. Youssef
MaRDI profile type: Publication
cites work: The theory of quasi-Sasakian structures
cites work: Contact manifolds in Riemannian geometry
cites work: Q4725286
cites work: A classification of almost contact metric manifolds
cites work: Q4774706
cites work: The sixteen classes of almost Hermitian manifolds and their linear invariants
cites work: Almost contact structures and curvature tensors
cites work: A class of almost contact Riemannian manifolds
cites work: Sur les structures presque complexes et autres structures infinitésimales régulières
cites work: Q3750580
cites work: Normal almost contact metric manifolds of dimension three
cites work: On differentiable manifolds with certain structures which are closely related to almost contact structure. II
cites work: On differentiable manifolds with contact metric structures
cites work: On locally conformal almost Kaehler manifolds
cites work: Q3892907
cites work: Generalized Hopf manifolds
description: scientific article; zbMATH DE number 169832