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

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:

Integrability conditions, Sasaki Metrics Tachibana operators, Almost Paracomplex structure, Tensor Bundle.,

PDF

___

[1] H. Çayır, Some Notes on Lifts of Almost Paracontact Structures, American Review of Mathematics and Statistics, 3 (2015). no.1, 52-60 .
[2] H. Çayır and K. Akdağ, Some notes on almost paracomplex structures associated with the diagonal lifts and operators on cotangent bundle , New Trends in Mathematical Sciences. 4 (2016). no. 4, 42-50.
[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.
[9] K.P. Mok, Lifts of vector fields to tensor bundles, Geom. Dedicata, 8 (1976). no. 1, 61-67.
[10] A.A. Salimov, Tensor Operators and Their applications, Nova Science Publ., New York, 2013.
[11] A.A. Salimov and A. Gezer, On the Geometry of the -Tensor Bundle with Sasaki Type Metric, Chin. Ann. Math., 32 (2011) B(3), 369-386.
[12] J. Szilasi, Notes on tensorial connections, Publ. Math. Debrecen, 31 (1984). no. (1-2), 29-37.
[13] K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker, New York, 1973.

Sigma Mühendislik ve Fen Bilimleri Dergisi-Cover

ISSN: 1304-7191
Yayın Aralığı: Yılda 4 Sayı
Yayıncı: Yıldız Teknik Üniversitesi

Arşiv