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## DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$

#### HAŞİM ÇAYIR [1] , MOHAMMAD NAZRUL ISLAM KHAN [2]

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In this paper, we define the Cheeger-Gromoll metric in the $(1,1)$ $-$tensor bundle $T_{1}^{1}(M)$, which is completely determined by its action on vector fields of type $X^{H}$ and $\omega ^{V}$. Later, we obtain the covarient and Lie derivatives applied to the Cheeger-Gromoll metric with respect to the horizontal and vertical lifts of vector and kovector fields, respectively.

(1 1)-tensor bundle,Covarient Derivative,Lie Derivative,Cheeger-Gromoll metric,Horizontal Lift,Vertical Lift
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Konular Mühendislik ve Temel Bilimler Articles Yazar: HAŞİM ÇAYIRE-posta: hasim.cayir@giresun.edu.trÜlke: Turkey Yazar: MOHAMMAD NAZRUL ISLAM KHANE-posta: m.nazrul@qu.edu.saÜlke: Saudi Arabia
 Bibtex @araştırma makalesi { konuralpjournalmath343519, journal = {Konuralp Journal of Mathematics}, issn = {}, address = {Mehmet Zeki SARIKAYA}, year = {2017}, volume = {5}, pages = {78 - 86}, doi = {}, title = {DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC \$\^\{CG\}g\$ ON THE \$(1,1)-\$TENSOR BUNDLE \$T\_\{1\}\^\{1\}(M)\$}, key = {cite}, author = {KHAN, MOHAMMAD NAZRUL ISLAM and ÇAYIR, HAŞİM} } APA ÇAYIR, H , KHAN, M . (2017). DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$. Konuralp Journal of Mathematics, 5 (2), 78-86. Retrieved from http://dergipark.gov.tr/konuralpjournalmath/issue/28490/343519 MLA ÇAYIR, H , KHAN, M . "DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$". Konuralp Journal of Mathematics 5 (2017): 78-86 Chicago ÇAYIR, H , KHAN, M . "DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$". Konuralp Journal of Mathematics 5 (2017): 78-86 RIS TY - JOUR T1 - DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$ AU - HAŞİM ÇAYIR , MOHAMMAD NAZRUL ISLAM KHAN Y1 - 2017 PY - 2017 N1 - DO - T2 - Konuralp Journal of Mathematics JF - Journal JO - JOR SP - 78 EP - 86 VL - 5 IS - 2 SN - -2147-625X M3 - UR - Y2 - 2017 ER - EndNote %0 Konuralp Journal of Mathematics DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$ %A HAŞİM ÇAYIR , MOHAMMAD NAZRUL ISLAM KHAN %T DERIVATIVES WITH RESPECT TO HORIZONTAL AND VERTICAL LIFTS OF THE CHEEGER-GROMOLL METRIC $^{CG}g$ ON THE $(1,1)-$TENSOR BUNDLE $T_{1}^{1}(M)$ %D 2017 %J Konuralp Journal of Mathematics %P -2147-625X %V 5 %N 2 %R %U