Article
2021
·
0 citations
On the geometry of tangent bundle of a hypersurface in R<SUP><i>n</i>+1</SUP>
Abstract
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.
Keywords
Tangent bundle
hypersurface
rescaled induced metric
curvature tensor
orthonormal frame
METRICS
CURVATURE
WoS Categories
Mathematics
Citation
- Journal
- TURKISH JOURNAL OF MATHEMATICS
- Year
- 2021
- Volume
- 45
- Issue
- 5
- Pages
- 2008-2024
- ISSN
- 1300-0098
- eISSN
- 1303-6149
- DOI
- 10.3906/mat-2102-52
- WoS UID
- WOS:000696961700001