On the geometry of tangent bundle of a hypersurface in Rn+1

Yurttançıkmaz S.

TURKISH JOURNAL OF MATHEMATICS, cilt.45, ss.2008-2024, 2021 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3906/mat-2102-52
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.2008-2024
  • Anahtar Kelimeler: Tangent bundle, hypersurface, rescaled induced metric, curvature tensor, orthonormal frame, METRICS, CURVATURE
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this paper, tangent bundle TM of the hypersurface M in Rn+1 has been studied. For hypersurface M given by immersion f : M -> Rn+1, considering the fact that F = df : TM -> R2n+2 is also immersion, TM is treated as a submanifold of R2n+2. Firstly, an induced metric which is called rescaled induced metric has been defined on TM, and the Levi-Civita connection has been calculated for this metric. Next, curvature tensors of tangent bundle TM have been obtained. Finally, the orthonormal frame at the point (p, u) is an element of TM has been defined and some curvature properties of such a tangent bundle by means of orthonormal frame for a given point have been investigated.