Statistical structures on tangent bundles and Lie groupps

Peyghan E., Seifipour D., GEZER A.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.50, sa.4, ss.1140-1154, 2021 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 4
  • Basım Tarihi: 2021
  • Doi Numarası: 10.15672/hujms.645070
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1140-1154
  • Anahtar Kelimeler: metric, &nbsp, statistical structure, tangent bundle, tangent Lie group, lift connection, G-NATURAL METRICS
  • Atatürk Üniversitesi Adresli: Evet

Özet

Let TM be a tangent bundle over a Riemannian manifold M with a Riemannian metric g and TG be a tangent Lie group over a Lie group with a left-invariant metric g. The purpose of the paper is two folds. Firstly, we study statistical structures on the tangent bundle TM equipped with two Riemannian g-natural metrics and lift connections. Secondly, we define a left-invariant complete lift connection on the tangent Lie group TG equipped with metric ge introduced in [F. Asgari and H. R. Salimi Moghaddam, On the Riemannian geometry of tangent Lie groups, Rend. Circ. Mat. Palermo II. Series, 2018] and study statistical structures in this setting.