Almost alpha-paracosymplectic manifolds

Erken I. K., Dacko P., Murathan C.

JOURNAL OF GEOMETRY AND PHYSICS, vol.88, pp.30-51, 2015 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 88
  • Publication Date: 2015
  • Doi Number: 10.1016/j.geomphys.2014.09.011
  • Journal Name: JOURNAL OF GEOMETRY AND PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.30-51
  • Keywords: Almost paracontact metric manifold, Almost paracosymplectic manifold, Almost para-Kenmotsu manifold, Para-Kaehler manifold, VECTOR-FIELDS, COSYMPLECTIC MANIFOLDS, HARMONICITY
  • Bursa Uludag University Affiliated: Yes

Abstract

This paper is a complete study of almost alpha-paracosymplectic manifolds. Basic properties of such manifolds are obtained and general curvature identities are proved. The manifolds with para-Kaehler leaves are characterized. It is proved that, for dimensions greater than 3, almost alpha-paracosymplectic manifolds are locally conformal to almost paracosymplectic manifolds and locally D-homothetic to almost para-Kenmotsu manifolds. Furthermore, it is proved that characteristic (Reeb) vector field xi is harmonic on almost alpha-para-Kenmotsu manifold if and only if it is an eigenvector of the Ricci operator. It is showed that almost alpha-para-Kenmotsu (kappa, mu, nu)-space has para-Kaehler leaves. 3-dimensional almost alpha-para-Kenmotsu manifolds are classified. As an application, it is obtained that 3-dimensional almost alpha-para-Kenmotsu manifold is (kappa, mu, nu)-space on an every open and dense subset of the manifold if and only if Reeb vector field is harmonic. Furthermore, examples are constructed. (C) 2014 Elsevier B.V. All rights reserved.