On almost paracontact Riemannian manifolds of type \((n,n)\)
type: Item
instance of: scholarly article
title: On almost paracontact Riemannian manifolds of type \((n,n)\)
zbMATH Open document ID: 1009.53024
author: Mancho Manev
author: Maria Staikova
published in: Journal of Geometry
publication date: 2003-04-27T00:00:00Z
review text: A \((2n+1)\)-dimensional differentiable manifold \(M\) is said to have an almost paracontact structure \((\varphi,\xi,\eta)\), if it admits a \((1,1)\)-tensor \(\varphi\), a vector field \(\xi\) and a 1-form \(\eta\) satisfying the following conditions: \[ \eta(\xi)=1, \quad \varphi^2= I_{2n+1}-\eta \otimes\xi, \quad tr\varphi =0. \] A positive definite Riemannian metric \(g\) is said to be compatible with the almost paracontact structure if it satisfies the following conditions: \[ g(\cdot,\xi) =\eta(\cdot),\;g(\varphi \cdot, \varphi\cdot) =g-\eta \otimes\eta. \] Then, \((\varphi,\xi,\eta,g)\) is called an almost paracontact Riemannian structure of type \((n,n)\). In this paper the authors give a classification with eleven basic classes of almost paracontact Riemannian manifolds of type \((n,n)\) with respect to the covariant derivative of the \((1,1)\)-tensor of the almost paracontact structure.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 1760628
zbMATH Keywords: vector field
zbMATH Keywords: 1-form
zbMATH Keywords: almost paracontact structure
zbMATH Keywords: covariant derivative
reviewed by: Domenico Perrone
Wikidata QID: Q115390036
MaRDI profile type: Publication
full work available at URL: s00022-001-8572-2
OpenAlex ID: W2025274871
DOI: 10.1007/S00022-001-8572-2
description: scientific article; zbMATH DE number 1760628