Some notes concerning Riemannian metrics of Cheeger Gromoll type

GEZER A., Altunbas M.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.396, sa.1, ss.119-132, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 396 Sayı: 1
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.jmaa.2012.06.011
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.119-132
  • Anahtar Kelimeler: Geodesic, Killing vector field, Paraholomorphic tensor field, Para-Kahler-Norden metric, TANGENT-BUNDLES, MANIFOLDS, CURVATURE, GEOMETRY
  • Atatürk Üniversitesi Adresli: Evet

Özet

Let (M, g) be an n-dimensional Riemannian manifold and TM its tangent bundle. The purpose of the present paper is three-fold. Firstly, to study paraholomorphy property of two Riemannian metrics g(a) and g(a,b) of Cheeger Gromoll type depending on one parameter and two parameters by using compatible paracomplex structures J(a) and J(a,b) on the tangent bundle TM. Secondly, to classify Killing vector fields on the tangent bundle TM equipped with the Riemannian metric g(a,b). Finally, to give a detailed description of geodesics on the tangent bundle TM with respect to the Riemannian metric g(a,b). (C) 2012 Elsevier Inc. All rights reserved.