Abstract
In this paper, we define a Sasakian metric ^{S}g on cotangent bundle T^{∗}Mⁿ, which is completely determined by its action on complete lifts of vector fields. Later, we obtain the covariant and Lie derivatives applied to Sasakian metrics with respect to the complete and vertical lifts of vector and kovector fields, respectively
Keywords
Covarient derivative Lie derivative Sasakian metric vertical lift complete lift horizontal lift
References
- Akyol, M.A., Gündüzalp, Y., Semi-Slant Submersions from Almost Product Riemannian Manifolds, Gulf Journal of Mathematics, 4(3), (2016), 15-27.
- Akyol, M.A., Gündüzalp, Y., Semi-Invariant Semi-Riemannian Submersions, Commun. Fac. Sci. Univ. Ank. Series A1, Volume 67, Number 1, (2018), 80-92.
- Cengiz, N., Salimov, A.A., Diagonal Lift in the Tensor Bundle and its Applications, Applied Mathematics and Computation, 142, (2003), 309-319.
- Çayır, H., Lie derivatives of almost contact structure and almost paracontact structure with respect to X^{V} and X^{H} on tangent bundle T(M), Proceedings of the Institute of Mathematics and Mechanics, 42(1), (2016), 38-49.
- Çayır, H., Tachibana and Vishnevskii Operators Applied to X^{V} and X^{C} in Almost Paracontact Structure on Tangent Bundle T(M), Ordu Üniversitesi Bilim ve Teknoloji Dergisi, 6(1), (2016), 67-82.
- Çayır, H., Tachibana and Vishnevskii Operators Applied to X^{V} and X^{H} in Almost Paracontact Structure on Tangent Bundle T(M), New Trends in Mathematical Sciences, 4(3), (2016), 105-115.
- Çayır, H., Köseoğlu, G., Lie Derivatives of Almost Contact Structure and Almost Paracontact Structure With Respect to X^{C} and X^{V} on Tangent Bundle T(M). New Trends in Mathematical Sciences, 4(1), (2016), 153-159.
- Gudmundsson, S., Kappos, E., On the Geometry of the Tangent Bundles, Expo. Math., 20, (2002), 1-41.
- Musso, E., Tricerri, F., Riemannian Metric on Tangent Bundles, Ann. Math. Pura. Appl., 150(4), (1988), 1-9.
- Ocak, F., Salimov, A.A., Geometry of the cotangent bundle with Sasakian metricsand its applications, Proc. Indian Acad. Sci. (Math. Sci.), 124(3), (2014), 427--436.
- Salimov, A.A., Tensor Operators and Their applications, Nova Science Publ., New York 2013.
- Salimov, A.A., Cengiz, N., Lifting of Riemannian Metrics to Tensor Bundles, Russian Math. (IZ. VUZ.) 47 (11), (2003), 47-55.
- Salimov, A.A., Filiz, A., Some Properties of Sasakian Metrics in Cotangent Bundles, Mediterr. J. Math. 8, (2011) 243-255.
- Sasaki, S., On The Differantial Geometry of Tangent Boundles of Riemannian Manifolds, Tohoku Math. J., 10, (1958), 338-358.
- Soylu, Y., A Myers-type compactness theorem by the use of Bakry-Emery Ricci tensor, Differ. Geom. Appl., 54, (2017), 245--250.
- Soylu, Y., A compactness theorem in Riemannian manifolds, J. Geom., 109:20,(2018).
- Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker Inc, New York 1973.
Abstract
References
- Akyol, M.A., Gündüzalp, Y., Semi-Slant Submersions from Almost Product Riemannian Manifolds, Gulf Journal of Mathematics, 4(3), (2016), 15-27.
- Akyol, M.A., Gündüzalp, Y., Semi-Invariant Semi-Riemannian Submersions, Commun. Fac. Sci. Univ. Ank. Series A1, Volume 67, Number 1, (2018), 80-92.
- Cengiz, N., Salimov, A.A., Diagonal Lift in the Tensor Bundle and its Applications, Applied Mathematics and Computation, 142, (2003), 309-319.
- Çayır, H., Lie derivatives of almost contact structure and almost paracontact structure with respect to X^{V} and X^{H} on tangent bundle T(M), Proceedings of the Institute of Mathematics and Mechanics, 42(1), (2016), 38-49.
- Çayır, H., Tachibana and Vishnevskii Operators Applied to X^{V} and X^{C} in Almost Paracontact Structure on Tangent Bundle T(M), Ordu Üniversitesi Bilim ve Teknoloji Dergisi, 6(1), (2016), 67-82.
- Çayır, H., Tachibana and Vishnevskii Operators Applied to X^{V} and X^{H} in Almost Paracontact Structure on Tangent Bundle T(M), New Trends in Mathematical Sciences, 4(3), (2016), 105-115.
- Çayır, H., Köseoğlu, G., Lie Derivatives of Almost Contact Structure and Almost Paracontact Structure With Respect to X^{C} and X^{V} on Tangent Bundle T(M). New Trends in Mathematical Sciences, 4(1), (2016), 153-159.
- Gudmundsson, S., Kappos, E., On the Geometry of the Tangent Bundles, Expo. Math., 20, (2002), 1-41.
- Musso, E., Tricerri, F., Riemannian Metric on Tangent Bundles, Ann. Math. Pura. Appl., 150(4), (1988), 1-9.
- Ocak, F., Salimov, A.A., Geometry of the cotangent bundle with Sasakian metricsand its applications, Proc. Indian Acad. Sci. (Math. Sci.), 124(3), (2014), 427--436.
- Salimov, A.A., Tensor Operators and Their applications, Nova Science Publ., New York 2013.
- Salimov, A.A., Cengiz, N., Lifting of Riemannian Metrics to Tensor Bundles, Russian Math. (IZ. VUZ.) 47 (11), (2003), 47-55.
- Salimov, A.A., Filiz, A., Some Properties of Sasakian Metrics in Cotangent Bundles, Mediterr. J. Math. 8, (2011) 243-255.
- Sasaki, S., On The Differantial Geometry of Tangent Boundles of Riemannian Manifolds, Tohoku Math. J., 10, (1958), 338-358.
- Soylu, Y., A Myers-type compactness theorem by the use of Bakry-Emery Ricci tensor, Differ. Geom. Appl., 54, (2017), 245--250.
- Soylu, Y., A compactness theorem in Riemannian manifolds, J. Geom., 109:20,(2018).
- Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker Inc, New York 1973.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Submission Date | March 7, 2018 |
| Acceptance Date | April 11, 2018 |
| Publication Date | February 1, 2019 |
| Published in Issue | Year 2019 Volume: 68 Issue: 1 |
Cite
Cited By
Geodesics and Torsion Tensor according to g-lift of Riemannian Connection on Cotangent Bundle
Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi
https://doi.org/10.21597/jist.622820
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
