SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2013 / Volume: 62 Issue: 2

ON LORENTZIAN TRANS-SASAKIAN MANIFOLDS

U.c. De
Krishnendu De
Pages
—
Publication Date
2013-08-01
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Next, in three- dimensional Lorentzian TransSasakian manifolds, explicit formulae for Ricci operator, Ricci tensor andcurvature tensor are obtained.Lorentzian Trans-Sasakian manifold of type ( ; ) is locallyand only if the scalar curvature r is constant providedFinally, we give some examples of three-dimensional Lorentzian Trans-Sasakianmanifold

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The object of the present paper is to study the Trans-Sasakianstructure on a manifold with Lorentzian metric.
📊
Key Findings & Data:Several interesting results areobtained on the manifold.
💡
Conclusion & Impact:Next, in three- dimensional Lorentzian TransSasakian manifolds, explicit formulae for Ricci operator, Ricci tensor andcurvature tensor are obtained.Lorentzian Trans-Sasakian manifold of type ( ; ) is locallyand only if the scalar curvature r is constant providedFinally, we give some examples of three-dimensional Lorentzian Trans-Sasakianmanifold
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:Lorentzian Trans-Sasakian manifold · -Einstein manifold · conformally *at manifold

Abstract

The object of the present paper is to study the Trans-Sasakianstructure on a manifold with Lorentzian metric. Several interesting results areobtained on the manifold. Also conformally *at Lorentzian Trans-Sasakianmanifolds have been studied. Next, in three- dimensional Lorentzian TransSasakian manifolds, explicit formulae for Ricci operator, Ricci tensor andcurvature tensor are obtained.Lorentzian Trans-Sasakian manifold of type ( ; ) is locallyand only if the scalar curvature r is constant providedFinally, we give some examples of three-dimensional Lorentzian Trans-Sasakianmanifold

🔖

Cite This Article

De, U., De, K. (2013). ON LORENTZIAN TRANS-SASAKIAN MANIFOLDS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 62 Issue: 2. https://doi.org/10.1501/Commua1_0000000697

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (23)

  1. Blair, D. E., Contact manifolds in Riemannian geometry, Lecture Notes in Math., Springer Verlag, (509)1976.
  2. Blair, D. E.and Oubina, J.A., Conformal and related changes of metric on the product of two almost contact metric manifolds, Publ. Mat.34(1)(1990), 199
  3. De, U.C.and Tripathi,M.M., Ricci tensor in 3-dimensional trans-Sasakian manifolds, Kyungpook Math.J.43(2)(2003),247
  4. Janssen, D. and Vanhecke, L., Almost contact structures and curvature tensors, Kodai Math. J.,4(1981),1
  5. Gill, H. and Dube, K.K., Generalized CR- Submanifolds of a trans Lorentzian para Sasakian manifold, Proc. Nat. Acad. Sci. India Sec. A Phys. 2(2006), 119
  6. Gray, A. and Hervella, L.M., The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Math. Pura Appl., (4) 123 (1980), 35
  7. Ikawa, T. and Erdogan, M., Sasakian manifolds with Lorentzian metric, Kyungpook Math. J. 35(1996), 517
  8. Marrero, J.C., The local structure of trans-sasakian manifolds, Ann.Mat.Pura Appl.(4)162 (1992),77-86.
  9. Matsumoto, K., On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Nat. Science, (1989), 151
  10. Matsumoto,K. and Mihai,I., On a certain transformation in a Lorentzian Para-Sasakian Manifold, Tensor (N.S.), 47(1988), 189
  11. Matsumoto, K., Mihai,I. and Rosca, R., -null geodesic gradient vector …elds on a Lorentzian para-Sasakian manifold. J. Korean Math. Soc. 32(1995), 17
  12. Mihai, I., Oiaga, A. and Rosca, R., Lorentzian Kenmotsu manifolds having two skew- sym- metric conformal vector …elds, Bull. Math. Soc. Sci. Math. Roumania, 42(1999), 237
  13. Mihai,I. and Rosca, R., On Lorentzian P-Sasakian Manifolds, Classical Analysis. World Scienti…c, Singapore, 1992 155
  14. Oubina, J.A., New classes of almost contact metric structures, Publicationes Mathematicae Debrecen 32 (1985), 21
  15. Shaikh, A. A., Baishya, K. K. and Eyasmin, S., On D-homothetic deformation of trans- sasakian structure, Demonstratio Mathematica, 1 2008, 171
  16. Takahashi, T., Sasakian symmetric spaces, Tohoku Math.J.(2)29, (1)(1977),91-113.
  17. Yaliniz, A.F., Yildiz, A. and Turan, M., On three-dimensional Lorentzian Kenmotsu manifolds, Kuwait J. Sci. Eng. 36 (2009), 51
  18. Yildiz, A., Turan, M. and Murathan, C., A class of Lorentzian Sasakian manifolds, Kyungpook Math. J. 49(2009), 789
  19. Current address: Uday Chand De,, Department of Pure Mathematics,, Calcutta University,, Kol, Krishnendu De, Konnagar High School(H.S.),, 68 G.T. Road (West),Konnagar,Hooghly, Pin.712235, West Bengal, INDIA. Road,,West Bengal, INDIA.
  20. E-mail address: [email protected], [email protected] URL: http://communications.science.ankara.edu.tr/index.php?series=A1
  21. Matsumoto, K., Mihai,I. and Rosca, R., -null geodesic gradient vector …elds on a Lorentzian para-Sasakian manifold. J. Korean Math. Soc. 32(1995), 17
  22. Current address: Uday Chand De,, Department of Pure Mathematics,, Calcutta University,, Kol, Krishnendu De, Konnagar High School(H.S.),, 68 G.T. Road (West),Konnagar,Hooghly, Pin.712235, West Bengal, INDIA. Road,,West Bengal, INDIA.
  23. E-mail address: [email protected], [email protected] URL: http://communications.science.ankara.edu.tr/index.php?series=A1