Research Article
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Year 2019, , 241 - 249, 03.10.2019
https://doi.org/10.36890/iejg.542783

Abstract

References

  • \bibitem{1} Aslanci, S., Cakan, R., On a cotangent bundle with deformed Riemannian extension, \emph{Mediterr. J. Math.} 11 (2014), 1251-1260.
  • \bibitem{2} Aslanci, S., Kazimova, S., Salimov, A.A., Some Remarks Concerning Riemannian Extensions, \emph{Ukrainian. Math. J.} 62, (2010), 661-675.
  • \bibitem{3}Bejan, C.L., Eken, \c{S}., A characterization of the Riemann extension in terms of harmonicity, \emph{Czech. Math. J.} 67, (2017), 197-206.
  • \bibitem{4}Bejan, C.L., Meri\c{c}, \c{S}. E., K{\i}l{\i}\c{c}, E., Einstein Metrics Induced by Natural Riemann Extensions, \emph{Adv. Appl. Clifford Algebras.} 27, (2017), 2333-2343.
  • \bibitem{5}Calvi\~{n}o-Louzao, E., Garc\'{i}a-R\'{i}o, E., Gilkey, P., V\'{a}zquez-Lorenzo A., The Geometry of Modified Riemannian Extensions, \emph{Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.} 465, (2009), 2023-2040.
  • \bibitem{6} Cruceanu, V., Fortuny, P., Gadea, M., A survey on paracomplex Geometry, \emph{Rocky Mountain J. Math.} 26, (1995), 83-115.
  • \bibitem{7} Dryuma, V., The Riemann Extensions in Theory of Differential Equations and their Applications, \emph{Mat. Fiz. Anal. Geom.} 10, (2003), 307-325.
  • \bibitem{8} Gezer, A., Bilen, L., Cakmak, A., Properties of Modified Riemannian Extensions,\emph{ Zh. Mat. Fiz. Anal. Geom.} 11, (2015), 159-173.
  • \bibitem{9} Kruckovic, GI., Hypercomplex structures on manifolds I. \emph{Trudy. Sem. Vektor Tenzor Anal.} 16, (1972), 174-201(in Russian).
  • \bibitem{10} Ocak, F., Kazimova, S., On a new metric in the cotangent bundle, \emph{Transactions of NAS of Azerbaijan Series of Physical-Technical and Mathematical Sciences.} 38, (2018), 128-138.
  • \bibitem{11} Patterson, E.M., Walker, A.G., Riemann Extensions, \emph{Quart. J. Math. Oxford Ser.} 3, (1952), 19–28.
  • \bibitem{12}Salimov, A., Tensor Operators and Their Applications, Nova Science Publishers, New York, USA, 2012.
  • \bibitem{13} Salimov, A., Cakan, R., On deformed Riemannian extensions associated with twin Norden metrics, \emph{Chinese Annals of Mathematics Series B. } 36, (2015), 345-354.
  • \bibitem{14} Salimov, A.A., Iscan, M., Akbulut, K., Notes on para-Norden–Walker 4-manifolds, \emph{International Journal of Geometric Methods in Modern Physics.} 7, (2010), 1331-1347.
  • \bibitem{15} Salimov, A. A., Iscan, M. and Etayo, F., Paraholomorphic B-manifold and its properties, \emph{Topology Appl.} 154,(2007), 925-933.
  • \bibitem{16} Yano, K., Ako, M., On certain operators associated with tensor fields, \emph{Kodai Math. Sem. Rep.} 20, (1968), 414-436.
  • \bibitem{17} Yano, K. and Ishihara, S., Tangent and Cotangent Bundles, Pure and Applied Mathematics, 16, Marcel Dekker, Inc., New York, 1973.

Notes About a New Metric on the Cotangent Bundle

Year 2019, , 241 - 249, 03.10.2019
https://doi.org/10.36890/iejg.542783

Abstract

In this article, we construct a new metric $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}  \over G}  = {}^R\nabla  + \sum\limits_{i,j = 1}^m {a^{ji}} \delta {p_j}\delta {p_i}$  in the cotangent  bundle, where ${}^R\nabla $ is the  Riemannian extension and  $ a^{ji}$ is a symmetric (2,0)-tensor field on a differentiable manifold.

References

  • \bibitem{1} Aslanci, S., Cakan, R., On a cotangent bundle with deformed Riemannian extension, \emph{Mediterr. J. Math.} 11 (2014), 1251-1260.
  • \bibitem{2} Aslanci, S., Kazimova, S., Salimov, A.A., Some Remarks Concerning Riemannian Extensions, \emph{Ukrainian. Math. J.} 62, (2010), 661-675.
  • \bibitem{3}Bejan, C.L., Eken, \c{S}., A characterization of the Riemann extension in terms of harmonicity, \emph{Czech. Math. J.} 67, (2017), 197-206.
  • \bibitem{4}Bejan, C.L., Meri\c{c}, \c{S}. E., K{\i}l{\i}\c{c}, E., Einstein Metrics Induced by Natural Riemann Extensions, \emph{Adv. Appl. Clifford Algebras.} 27, (2017), 2333-2343.
  • \bibitem{5}Calvi\~{n}o-Louzao, E., Garc\'{i}a-R\'{i}o, E., Gilkey, P., V\'{a}zquez-Lorenzo A., The Geometry of Modified Riemannian Extensions, \emph{Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.} 465, (2009), 2023-2040.
  • \bibitem{6} Cruceanu, V., Fortuny, P., Gadea, M., A survey on paracomplex Geometry, \emph{Rocky Mountain J. Math.} 26, (1995), 83-115.
  • \bibitem{7} Dryuma, V., The Riemann Extensions in Theory of Differential Equations and their Applications, \emph{Mat. Fiz. Anal. Geom.} 10, (2003), 307-325.
  • \bibitem{8} Gezer, A., Bilen, L., Cakmak, A., Properties of Modified Riemannian Extensions,\emph{ Zh. Mat. Fiz. Anal. Geom.} 11, (2015), 159-173.
  • \bibitem{9} Kruckovic, GI., Hypercomplex structures on manifolds I. \emph{Trudy. Sem. Vektor Tenzor Anal.} 16, (1972), 174-201(in Russian).
  • \bibitem{10} Ocak, F., Kazimova, S., On a new metric in the cotangent bundle, \emph{Transactions of NAS of Azerbaijan Series of Physical-Technical and Mathematical Sciences.} 38, (2018), 128-138.
  • \bibitem{11} Patterson, E.M., Walker, A.G., Riemann Extensions, \emph{Quart. J. Math. Oxford Ser.} 3, (1952), 19–28.
  • \bibitem{12}Salimov, A., Tensor Operators and Their Applications, Nova Science Publishers, New York, USA, 2012.
  • \bibitem{13} Salimov, A., Cakan, R., On deformed Riemannian extensions associated with twin Norden metrics, \emph{Chinese Annals of Mathematics Series B. } 36, (2015), 345-354.
  • \bibitem{14} Salimov, A.A., Iscan, M., Akbulut, K., Notes on para-Norden–Walker 4-manifolds, \emph{International Journal of Geometric Methods in Modern Physics.} 7, (2010), 1331-1347.
  • \bibitem{15} Salimov, A. A., Iscan, M. and Etayo, F., Paraholomorphic B-manifold and its properties, \emph{Topology Appl.} 154,(2007), 925-933.
  • \bibitem{16} Yano, K., Ako, M., On certain operators associated with tensor fields, \emph{Kodai Math. Sem. Rep.} 20, (1968), 414-436.
  • \bibitem{17} Yano, K. and Ishihara, S., Tangent and Cotangent Bundles, Pure and Applied Mathematics, 16, Marcel Dekker, Inc., New York, 1973.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Filiz Ocak 0000-0003-4157-6404

Publication Date October 3, 2019
Acceptance Date August 10, 2019
Published in Issue Year 2019

Cite

APA Ocak, F. (2019). Notes About a New Metric on the Cotangent Bundle. International Electronic Journal of Geometry, 12(2), 241-249. https://doi.org/10.36890/iejg.542783
AMA Ocak F. Notes About a New Metric on the Cotangent Bundle. Int. Electron. J. Geom. October 2019;12(2):241-249. doi:10.36890/iejg.542783
Chicago Ocak, Filiz. “Notes About a New Metric on the Cotangent Bundle”. International Electronic Journal of Geometry 12, no. 2 (October 2019): 241-49. https://doi.org/10.36890/iejg.542783.
EndNote Ocak F (October 1, 2019) Notes About a New Metric on the Cotangent Bundle. International Electronic Journal of Geometry 12 2 241–249.
IEEE F. Ocak, “Notes About a New Metric on the Cotangent Bundle”, Int. Electron. J. Geom., vol. 12, no. 2, pp. 241–249, 2019, doi: 10.36890/iejg.542783.
ISNAD Ocak, Filiz. “Notes About a New Metric on the Cotangent Bundle”. International Electronic Journal of Geometry 12/2 (October 2019), 241-249. https://doi.org/10.36890/iejg.542783.
JAMA Ocak F. Notes About a New Metric on the Cotangent Bundle. Int. Electron. J. Geom. 2019;12:241–249.
MLA Ocak, Filiz. “Notes About a New Metric on the Cotangent Bundle”. International Electronic Journal of Geometry, vol. 12, no. 2, 2019, pp. 241-9, doi:10.36890/iejg.542783.
Vancouver Ocak F. Notes About a New Metric on the Cotangent Bundle. Int. Electron. J. Geom. 2019;12(2):241-9.