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| On Affine Connections Induced on the (1,1)-Tensor Bundle |
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Citation： |
Murat ALTUNBAS,Aydin GEZER.On Affine Connections Induced on the (1,1)-Tensor Bundle[J].Chinese Annals of Mathematics B,2018,39(4):683~694 |
| Page view： 1337
Net amount： 699 |
Authors： |
Murat ALTUNBAS; Aydin GEZER |
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| Abstract： |
Let $M$ be an $n$-dimensional differentiable manifold with an affine
connection without torsion and $T_{1}^{1}(M)$ its $(1,1)$-tensor
bundle. In this paper, the authors define a new affine connection on
$T_{1}^{1}(M)$ called the intermediate lift connection, which lies
somewhere between the complete lift connection and horizontal lift
connection. Properties of this intermediate lift connection are
studied. Finally, they consider an affine connection induced from
this intermediate lift connection on a cross-section $\sigma _{\xi
}(M)$ of $T_{1}^{1}(M)$ defined by a $(1,1)$-tensor field $\xi $ and
present some of its properties. |
Keywords： |
Connections, Geodesic, Semi-symmetry type condition, Sasaki metric, Tensor bundle |
Classification： |
53C07, 53C22, 53C35 |
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