Research Article

Lifts of connections to the bundle of (1,1) type tensor frames

Volume: 39 Number: 2 June 2, 2021
  • Habil Fattayev1
  • Haşim Çayır

Lifts of connections to the bundle of (1,1) type tensor frames

Abstract

In this paper we consider the bundle of (1,1) type tensor frames over a smooth manifold, define the horizontal and complete lifts of symmetric linear connection into this bundle. Also we study the properties of the geodesic lines corresponding to the complete lift of the linear connection and investigate the relations between Sasaki metric and lifted connections on the bundle of (1,1) type tensor frames.

Keywords

References

  1. [1] L. A. Cordero, C. T. Dodson and Manuel de Leon, Differential Geometry of Frame Bundles, Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht, 1989.
  2. [2] L. A. Cordero and Manuel de Leon, Horizontal lift of connection to the frame bundle, Boll. Un. Mat. Ital 6 (1984), 223-240.
  3. [3] H. D. Fattayev, The lifts of affine connections to the bundle of (2,0) type contra-variant tensors, J. of Qafqaz Univ., 19(2007), 116-119.
  4. [4] H. D. Fattayev, Some problems of differential geometry of the bundle of affinor frames, News of Baku Univ., Physico-Math. Sci., 1(2018), 45-57.
  5. [5] H. D. Fattayev, The geodesic lines of the lifts of affine connections in the bundle of (2,0) type contravariant tensors, News of Baku Univ., Physico-Math. Sci., 3(2007) 52-57.
  6. [6] J. Kurek, On a horizontal lift of a linear connection to the bundle of linear frames, Ann. Univ. Marie Curie-Skladovska. Sectio A., XLI(1097), 31-37.
  7. [7] A. Mağden and A. A. Salimov, Geodesics for complete lifts of affine connections in tensor bundles, Appl. Math. and Comp., 151(2004), no. 3, 863-868.
  8. [8] K. P. Mok, Metrics and connections on the cotangent bundle, Kodai Math. Sem. Rep., 28 (1977), 226-238.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Habil Fattayev1 This is me
0000-0003-0861-3904
Azerbaijan

Haşim Çayır This is me
0000-0003-0348-8665
Türkiye

Publication Date

June 2, 2021

Submission Date

September 27, 2021

Acceptance Date

January 1, 2021

Published in Issue

Year 2021 Volume: 39 Number: 2

APA
Fattayev1, H., & Çayır, H. (2021). Lifts of connections to the bundle of (1,1) type tensor frames. Sigma Journal of Engineering and Natural Sciences, 39(2), 177-183. https://izlik.org/JA75CH85LT
AMA
1.Fattayev1 H, Çayır H. Lifts of connections to the bundle of (1,1) type tensor frames. SIGMA. 2021;39(2):177-183. https://izlik.org/JA75CH85LT
Chicago
Fattayev1, Habil, and Haşim Çayır. 2021. “Lifts of Connections to the Bundle of (1,1) Type Tensor Frames”. Sigma Journal of Engineering and Natural Sciences 39 (2): 177-83. https://izlik.org/JA75CH85LT.
EndNote
Fattayev1 H, Çayır H (June 1, 2021) Lifts of connections to the bundle of (1,1) type tensor frames. Sigma Journal of Engineering and Natural Sciences 39 2 177–183.
IEEE
[1]H. Fattayev1 and H. Çayır, “Lifts of connections to the bundle of (1,1) type tensor frames”, SIGMA, vol. 39, no. 2, pp. 177–183, June 2021, [Online]. Available: https://izlik.org/JA75CH85LT
ISNAD
Fattayev1, Habil - Çayır, Haşim. “Lifts of Connections to the Bundle of (1,1) Type Tensor Frames”. Sigma Journal of Engineering and Natural Sciences 39/2 (June 1, 2021): 177-183. https://izlik.org/JA75CH85LT.
JAMA
1.Fattayev1 H, Çayır H. Lifts of connections to the bundle of (1,1) type tensor frames. SIGMA. 2021;39:177–183.
MLA
Fattayev1, Habil, and Haşim Çayır. “Lifts of Connections to the Bundle of (1,1) Type Tensor Frames”. Sigma Journal of Engineering and Natural Sciences, vol. 39, no. 2, June 2021, pp. 177-83, https://izlik.org/JA75CH85LT.
Vancouver
1.Habil Fattayev1, Haşim Çayır. Lifts of connections to the bundle of (1,1) type tensor frames. SIGMA [Internet]. 2021 Jun. 1;39(2):177-83. Available from: https://izlik.org/JA75CH85LT

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