New structures of golden type on the tangent bundle

Druţă-Romaniuc S., Hreţcanu C., GEZER A.

Turkish Journal of Mathematics, cilt.49, sa.6, ss.850-871, 2025 (SCI-Expanded, Scopus, TRDizin) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 6
  • Basım Tarihi: 2025
  • Doi Numarası: 10.55730/1300-0098.3629
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.850-871
  • Anahtar Kelimeler: 53B35, 53C15, 53C55, almost (α, p) -golden Riemannian manifold, almost Hermitian structure, natural lift, Riemannian almost product structure, Tangent bundle, α -structure
  • Atatürk Üniversitesi Adresli: Evet

Özet

The aim of our paper is to prove the existence of some types of almost (α, p) -golden structures, obtained as general natural lifts of the Riemannian metric from the base manifold M to the total space TM of the tangent bundle. We show that TM , endowed with a general natural almost (α, p) -golden structure (which is a generalisation of the golden structure) and with a general natural metric, is an almost (α, p) -golden Riemannian manifold if and only if the function coefficients of the almost (α, p) -golden structure are related those of the metric by two systems of three equations each. When α = 1 we obtain five types of such manifolds and when α = −1 we show that TM is an almost (−1, p) -golden Riemannian manifold if and only if the function coefficients of the metric and of the (−1, p) -golden structure satisfy some proportionality relations.