Secoond order parallel tensors on some paracontact manifolds

Abstract

The object of the present paper is to study the symmetric and skewsymmetric 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 at 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 -para-Kenmotsu (k;μ)-space with k≠ 0, then it is a constant multiple of the associated metric tensor g of M²ⁿ⁺¹.

Mathematics Subject Classication (2010): 53C15, 53C25, 53D10, 53D15.

Key words: Second order parallel tensor, paracontact metric (k;μ)-space, almost -para-Kenmotsu (k;μ)-space.