Geodesics of Sasakian Metrics on Tensor Bundles

SALIMOV A., GEZER A., AKBULUT K.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.6, sa.2, ss.135-147, 2009 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6 Sayı: 2
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1007/s00009-009-0001-z
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.135-147
  • Anahtar Kelimeler: Geodesics, horizontal and vertical lift, Jacobi fields, Sasakian metric, tensor bundle, LIFTS
  • Atatürk Üniversitesi Adresli: Evet

Özet

On the basis of the phase completion the notion of vertical and horizontal lifts of vector fields is defined in the tensor bundles over a Riemannian manifold. Such a tensor bundle is made into a manifold with a Riemannian structure of special type by endowing it with Sasakian metric. The components of the Levi-Civita and other metric connections with respect to Sasakian metrics on tensor bundles with respect to the adapted frame are presented. This having been done, it is shown that it is possible to study geodesics of Sasakian metrics dealing with geodesics of the base manifolds.