ON THE GEOMETRY OF THE RESCALED RIEMANNIAN METRIC ON TENSOR BUNDLES OF ARBITRARY TYPE

GEZER A., Altunbas M.

KODAI MATHEMATICAL JOURNAL, cilt.38, sa.1, ss.37-64, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 1
  • Basım Tarihi: 2015
  • Doi Numarası: 10.2996/kmj/1426684442
  • Dergi Adı: KODAI MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.37-64
  • Anahtar Kelimeler: Almost product structure, geodesic, metric connection, pure metric, tensor bundle, HERMITIAN COTANGENT BUNDLES, GOLDEN RATIO, PRODUCT, INTEGRABILITY, 4-MANIFOLDS, LIFTS, SPACE
  • Atatürk Üniversitesi Adresli: Evet

Özet

Let (M, g) be an n-dimensional Riemannian manifold and T-1(1) (M) be its (1, 1)-tensor bundle equipped with the rescaled Sasaki type metric (s)g(f) which rescale the horizontal part by a non-zero differentiable function f. In the present paper, we discuss curvature properties of the Levi-Civita connection and another metric connection of T-1(1) (M). We construct almost product Riemannian structures on T-1(1)(M) and investigate conditions for these structures to be locally decomposable. Also, some applications concerning with these almost product Riemannian structures on T-1(1)(M) are presented. Finally we introduce the rescaled Sasaki type metric (s)g(f) on the (p, q)-tensor bundle and characterize the geodesics on the (p, q)-tensor bundle with respect to the Levi-Civita connection and another metric connection of (s)g(f).