Article

Second order parallel tensors on some paracontact manifolds

Published in: Quaestiones Mathematicae
Volume 40, issue 7, 2017, pages: 849–860
DOI: 10.2989/16073606.2017.1329239
Author(s): Ximin LiuSchool of Mathematical Sciences, China, Quanxiang PanSchool of Mathematical Sciences, China

Abstract

The object of the present paper is to study the symmetric and skew-symmetric properties of a second order parallel tensor on paracontact metric (k, µ)-spaces and almost β-para-Kenmotsu (k, µ)-spaces. In this paper, we prove that if there exists a second order symmetric parallel tensor on a paracontact metric (k, µ)-space M, then either M is locally isometric to a product of a flat n + 1-dimensional manifold and an n-dimensional manifold of constant sectional curvature 4, or the second order parallel tensor is a constant multiple of the associated metric tensor g of M2n+1. If there is a second order parallel tensor on an almost β-para-Kenmotsu (k, µ)-space with k ≠ 0, then it is a constant multiple of the associated metric tensor g of M2n+1.

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