Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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SASAKIAN METRICS, INTEGRABILITY CONDITIONS AND OPERATORS ON COTANGENT BUNDLE

  • CAYIR, Hasim (Department of Mathematics, Giresun University)
  • Received : 2018.05.19
  • Accepted : 2018.06.20
  • Published : 2018.12.25
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Abstract

In this paper firstly, It was studied almost paraholomorphic vector field with respect to almost para-Nordenian structure ($F^S$, g) and the purity conditions of the Sasakian metric is investigate with respect to almost para complex structure F on cotangent bundle. Secondly, we obtained the integrability conditions of almost paracomplex structure F by calculating the Nijenhuis tensors of F of type (1, 1) on $^CT(M_n)$. Finally, the Tachibana operator ${\phi}_{\varphi}$ applied to $^Sg$ according to F and the Vishnevskii operators (${\psi}_{\varphi}$-operator) applied to the vertical and horizontal lifts with respect to F on cotangent bundle.

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References

  1. M. A. Akyol and B. Sahin, Conformal anti-invariant submersions from almost Hermitian manifolds, Turkish Journal of Mathematics, 40(2016), 43-70. https://doi.org/10.3906/mat-1408-20
  2. H. Cayir, Some Notes on Lifts of Almost Paracontact Structures, American Review of Mathematics and Statistics, 3(1)(2015), 52-60.
  3. H. Cayir, Lie derivatives of almost contact structure and almost paracontact structure with respect to XV and XH on tangent bundle T(M), Proceedings of the Institute of Mathematics and Mechanics, 42 (1)(2016), 38-49.
  4. H. Cayir, Tachibana and Vishnevskii Operators Applied to XV and XC in Almost Paracontact Structure on Tangent Bundle T(M), Ordu Universitesi Bilim ve Teknoloji Dergisi, 6 (1)(2016), 67-82.
  5. H. Cayir, Tachibana and Vishnevskii Operators Applied to XV and XH in Almost Paracontact Structure on Tangent Bundle T(M), New Trends in Mathematical Sciences, 4(3)(2016), 105-115. https://doi.org/10.20852/ntmsci.2016318821
  6. H. Cayir and G. Koseoglu, Lie Derivatives of Almost Contact Structure and Almost Paracontact Structure With Respect to XC and XV on Tangent Bundle T(M), New Trends in Mathematical Sciences, 4 (1)(2016), 153-159. https://doi.org/10.20852/ntmsci.2016115657
  7. Y. Gunduzalp, Neutral slant submanifolds of a para-Kahler manifold. Abstract and Applied Analysis, 2013, Article Doi:10.1155/2013/752650, 1-8.
  8. A. Gezer, L. Bilen and A. Cakmak, Properties of Modified Riemannian Extensions, Journal of Mathematical Physics, Analysis, Geometry, 11(2)(2015), 159-173.
  9. G. I. Kruchkovich, Hypercomplex structure on manifold, Tr. Sem. Vect. Tens. Anal. Moscow Univ, 16(1972), 174-201.
  10. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry-Volume I. John Wiley & Sons, Inc, New York, 1963.
  11. A. A. Salimov, Tensor Operators and Their applications, Nova Science Publ. New York, 2013.
  12. B. Sahin and M. A. Akyol, Golden maps betwen Golden Riemannian manifolds and constancy of certain maps, Math Commun., 19(2014), 333-342.
  13. A. A. Salimov and H. Cayir, Some Notes On Almost Paracontact Structures, Comptes Rendus de 1'Acedemie Bulgare Des Science, 66(3)(2013), 331-338.
  14. A. A. Salimov, M. Iscan and F. Etayo, Paraholomorphic B-manifold and its properties, Topology and its Applications, 154(2007), 925-933. https://doi.org/10.1016/j.topol.2006.10.003
  15. A. A. Salimov and F. Agca, On para-Nordenian structures, Ann Polon Math, 99(2010), 193-200. https://doi.org/10.4064/ap99-2-6
  16. K. Yano and S. Ishihara, Tangent and Cotangent Bundles Differential geometry. Pure and Applied Mathematics. Mercel Dekker, Inc, New York, 1973.