SOME NOTES ON INTEGRABILITY CONDITIONS, SASAKI METRICS AND OPERATORS ON (1,1)-TENSOR BUNDLE

Haşim Çayır; Yasemin Soylu; Hülya Durur

SOME NOTES ON INTEGRABILITY CONDITIONS, SASAKI METRICS AND OPERATORS ON (1,1)-TENSOR BUNDLE

Abstract

The main purpose of the present paper is to study integrability conditions by calculating the Nijenhuis Tensors of almost paracomplex structure on Tensor Bundle. Later, we obtain the Lie derivatives applied to Sasakian metrics with respect to the horizontal and vertical lifts of vector and kovector fields, respectively. Finally, we get the results of Tachibana and Vishnevskii operators applied to horizontal and vertical lifts according to structure on Tensor Bundle .

Keywords

References

[1] H. Çayır, Some Notes on Lifts of Almost Paracontact Structures, American Review of Mathematics and Statistics, 3 (2015). no.1, 52-60 .
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[3] H. Çayır and G. Köseoğlu, Lie Derivatives of Almost Contact Structure and Almost Paracontact Structure With Respect to and on Tangent Bundle . New Trends in Mathematical Sciences, 4 (2016). no. 1, 153-159.
[4] N. Cengiz and A.A. Salimov, Complete lifts of derivations to tensor bundles, Bol. Soc. Mat. Mexicana, 8 (2002). no. 3, 75-82
[5] J. Gancarzewicz and N. Rahmani, Relevent horizontal des connexions linearies au fibre vectoriel associe avec le fibre principal des repres lineaires, Annales Polinici Math. 48 (1988). 281-289 .
[6] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry-Volume I, John Wiley Sons, Inc, New York, 1963.
[7] K.F. Lai and K.P. Mok, On the differential geometry of the tensor bundle, Tensor (New Series), 63 (2002), 15-27.
[8] A.J. Ledger and K. Yano, Almost complex structures on the tensor bundles, J. Diff. Geom. 1 (1967), 355-368.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

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

Yasemin Soylu This is me
0000-0001-9009-1214
Türkiye

Hülya Durur This is me
0000-0002-9297-6873
Türkiye

Publication Date

June 1, 2019

Submission Date

October 4, 2018

Acceptance Date

March 5, 2019

Published in Issue

Year 2019 Volume: 37 Number: 2

IZ

https://izlik.org/JA43KD47KW

Cite

RIS / Bibtex

APA

Çayır, H., Soylu, Y., & Durur, H. (2019). SOME NOTES ON INTEGRABILITY CONDITIONS, SASAKI METRICS AND OPERATORS ON (1,1)-TENSOR BUNDLE. Sigma Journal of Engineering and Natural Sciences, 37(2), 445-459. https://izlik.org/JA43KD47KW

AMA

1.Çayır H, Soylu Y, Durur H. SOME NOTES ON INTEGRABILITY CONDITIONS, SASAKI METRICS AND OPERATORS ON (1,1)-TENSOR BUNDLE. SIGMA. 2019;37(2):445-459. https://izlik.org/JA43KD47KW

Chicago

Çayır, Haşim, Yasemin Soylu, and Hülya Durur. 2019. “SOME NOTES ON INTEGRABILITY CONDITIONS, SASAKI METRICS AND OPERATORS ON (1,1)-TENSOR BUNDLE”. Sigma Journal of Engineering and Natural Sciences 37 (2): 445-59. https://izlik.org/JA43KD47KW.

EndNote

Çayır H, Soylu Y, Durur H (June 1, 2019) SOME NOTES ON INTEGRABILITY CONDITIONS, SASAKI METRICS AND OPERATORS ON (1,1)-TENSOR BUNDLE. Sigma Journal of Engineering and Natural Sciences 37 2 445–459.

IEEE

[1]H. Çayır, Y. Soylu, and H. Durur, “SOME NOTES ON INTEGRABILITY CONDITIONS, SASAKI METRICS AND OPERATORS ON (1,1)-TENSOR BUNDLE”, SIGMA, vol. 37, no. 2, pp. 445–459, June 2019, [Online]. Available: https://izlik.org/JA43KD47KW

ISNAD

Çayır, Haşim - Soylu, Yasemin - Durur, Hülya. “SOME NOTES ON INTEGRABILITY CONDITIONS, SASAKI METRICS AND OPERATORS ON (1,1)-TENSOR BUNDLE”. Sigma Journal of Engineering and Natural Sciences 37/2 (June 1, 2019): 445-459. https://izlik.org/JA43KD47KW.

JAMA

1.Çayır H, Soylu Y, Durur H. SOME NOTES ON INTEGRABILITY CONDITIONS, SASAKI METRICS AND OPERATORS ON (1,1)-TENSOR BUNDLE. SIGMA. 2019;37:445–459.

MLA

Çayır, Haşim, et al. “SOME NOTES ON INTEGRABILITY CONDITIONS, SASAKI METRICS AND OPERATORS ON (1,1)-TENSOR BUNDLE”. Sigma Journal of Engineering and Natural Sciences, vol. 37, no. 2, June 2019, pp. 445-59, https://izlik.org/JA43KD47KW.

Vancouver

1.Haşim Çayır, Yasemin Soylu, Hülya Durur. SOME NOTES ON INTEGRABILITY CONDITIONS, SASAKI METRICS AND OPERATORS ON (1,1)-TENSOR BUNDLE. SIGMA [Internet]. 2019 Jun. 1;37(2):445-59. Available from: https://izlik.org/JA43KD47KW