TY  - JOUR
T1  - On the Geometry of the Tangent Bundle With Vertical Rescaled Metric
AU  - Dida, Hamou Mohammed
AU  - Hathout, Fouzi
AU  - Azzouz, Abdelhalim
PY  - 2019
DA  - February
Y2  - 2017
DO  - 10.31801/cfsuasmas.443735
JF  - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
JO  - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
PB  - Ankara University
WT  - DergiPark
SN  - 1303-5991
SP  - 222
EP  - 235
VL  - 68
IS  - 1
LA  - en
AB  - Let (M,g) be a n-dimensional smooth Riemannian manifold. In the present paper, we introduce a new class of natural metrics denoted by G^{f} and called the vertical rescaled metric on the tangent bundle TM. We calculate its Levi-Civita connection and Riemannian curvature tensor. We study the geometry of (TM,G^{f}) and several important results are obtained on curvature, Einstein structure, scalar and sectional curvatures
KW  - Tangent bundle
KW  - vertical rescaled metric
KW  - Einstein structure
KW  - curvature
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UR  - https://doi.org/10.31801/cfsuasmas.443735
L1  - https://dergipark.org.tr/en/download/article-file/506499
ER  -