Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A NEW CLASS OF RIEMANNIAN METRICS ON TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD

  • Baghban, Amir (Facultu of Mathematics Azarbaijan Shahid Madani University) ;
  • Sababe, Saeed Hashemi (Young Researchers and Elite Club Malard Branch, Islamic Azad University)
  • Received : 2020.04.02
  • Accepted : 2020.07.24
  • Published : 2020.10.31
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Abstract

The class of isotropic almost complex structures, J𝛿,𝜎, define a class of Riemannian metrics, g𝛿,𝜎, on the tangent bundle of a Riemannian manifold which are a generalization of the Sasaki metric. This paper characterizes the metrics g𝛿,0 using the geometry of tangent bundle. As a by-product, some integrability results will be reported for J𝛿,𝜎.

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References

  1. M. T. K. Abbassi, G. Calvaruso, and D. Perrone, Harmonic sections of tangent bundles equipped with Riemannian g-natural metrics, Q. J. Math. 62 (2011), no. 2, 259-288. https://doi.org/10.1093/qmath/hap040
  2. M. T. K. Abbassi and M. Sarih, On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds, Differential Geom. Appl. 22 (2005), no. 1, 19-47. https://doi.org/10.1016/j.difgeo.2004.07.003
  3. R. M. Aguilar, Isotropic almost complex structures on tangent bundles, Manuscripta Math. 90 (1996), no. 4, 429-436. https://doi.org/10.1007/BF02568316
  4. A. Baghban and E. Abedi, On the integrability of the isotropic almost complex structures and harmonic unit vector fields, arXiv:1606.09198v1, 2016.
  5. A. Baghban and E. Abedi, Curvatures of metrics induced by the isotropic almost complex structures, arXiv preprint arXiv:1607.07018, 2016.
  6. A. Baghban and E. Abedi, A new class of almost complex structures on tangent bundle of a Riemannian manifold, Commun. Math. 26 (2018), no. 2, 137-145. https://doi.org/10.2478/cm-2018-0010
  7. I. Biswas, J. Loftin, and M. Stemmler, Flat bundles on affine manifolds, Arab. J. Math. (Springer) 2 (2013), no. 2, 159-175. https://doi.org/10.1007/s40065-012-0064-8
  8. J. Choi and A. P. Mullhaupt, Kahlerian information geometry for signal processing, Entropy 17 (2015), no. 4, 1581-1605. https://doi.org/10.3390/e17041581
  9. R. M. Friswell and C. M. Wood, Harmonic vector fields on pseudo-Riemannian manifolds, J. Geom. Phys. 112 (2017), 45-58. https://doi.org/10.1016/j.geomphys.2016.10.015
  10. C. Kuzu and N. Cengiz, Curvature tensor in tangette bundles of semi-riemannian manifold, NTMSCI 6 (2018), no. 3, 168-173.
  11. S. T. Lisi, Applications of symplectic geometry to Hamiltonian mechanics, ProQuest LLC, Ann Arbor, MI, 2006.
  12. E. Peyghan, A. Baghban, and E. Sharahi, Linear Poisson structures and Hom-Lie algebroids, Rev. Un. Mat. Argentina 60 (2019), no. 2, 299-313. https://doi.org/10.33044/ revuma.v60n2a01
  13. E. Peyghan, A. Heydari, and L. Nourmohammadi Far, On the geometry of tangent bundles with a class of metrics, Ann. Polon. Math. 103 (2012), no. 3, 229-246. https://doi.org/10.4064/ap103-3-2
  14. E. Peyghan, H. Nasrabadi, and A. Tayebi, The homogeneous lift to the (1, 1)-tensor bundle of a Riemannian metric, Int. J. Geom. Methods Mod. Phys. 10 (2013), no. 4, 1350006, 18 pp. https://doi.org/10.1142/S0219887813500060
  15. E. Peyghan and L. Nourmohammadi Far, Foliations and a class of metrics on tangent bundle, Turkish J. Math. 37 (2013), no. 2, 348-359. https://doi.org/10.3906/mat-1102-36
  16. A. Salimov and A. Gezer, On the geometry of the (1, 1)-tensor bundle with Sasaki type metric, Chin. Ann. Math. Ser. B 32 (2011), no. 3, 369-386. https://doi.org/10.1007/s11401-011-0646-3
  17. J. Zhang and F. Li, Symplectic and Kahler structures on statistical manifolds induced from divergence functions, in Geometric science of information, 595-603, Lecture Notes in Comput. Sci., 8085, Springer, Heidelberg, 2013. https://doi.org/10.1007/978-3-642-40020-9_66