Volume 68 | Issue 7 | Year 2022 | Article Id. IJMTT-V68I7P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I7P508
Received | Revised | Accepted | Published |
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07 Jun 2022 | 06 Jul 2022 | 14 Jul 2022 | 19 Jul 2022 |
In this paper we consider a quarter-symmetric metric connection in a ()-Lorentzian Para-Sasakian manifold and study Locally -symmetric, Locally concircular -symmetric and -concircularly flat ()-Lorentzian Para-Sasakian manifold with respect to a quarter-symmetric metric connection.
[1] Ajit Barman, On lorentzian-Sasakian manifolds admitting a type of semi-symmetric metric connection, Novi Sad J. Math. Vol. 44, No. 2, (2014), 77-88.
[2] D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics 509, Springer-Verlag 1976.
[3] U. C. De and A. Sarkar, On (ε)-Kenmotsu manifold, Hadronic J. 32 (2009), no. 2, 231-242.
[4] D. M. Naik, Venkatesha and D. G. Prakasha, Certain results on Kenmotsu pseudo-metric manifolds, Miskolc Mathematical Notes, Vol. 20 (2019), No. 2, pp. 1083-1099.
[5] A. Friedmann and J. A. Schouten, Uber die Geometrie der halbsymmetrischen Ubertragung, Math. Zeitschr. 21 (1924), 211-223.
[6] S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor, N.S. 29 (1975), 249-254.
[7] A. Hasseb, A. Prakash and M. D. Siddqi, On a Quarter-Symmetric Metric Connection in an(ε)Lorentzian Para-Sasakian Manifold, Acta. Math. Univ. Comenianae, Vol. LXXXVI, 1 (2017), pp. 143-152.
[8] C. Ozgur, Φ-projectively flat Lorentian para-Sasakian manifolds, Radovi Mathematicki 12 (2003) 1-8.
[9] K. T. Pradeep Kumar, C. S. Bagewadi and Venkatesha, On Projective Φ-symmetric K-contact manifold admitting quarter-symmetric metric connection, Differ. Geom. Dyn. Syst., 13, (2011), 128-137.
[10] D. G. Prakasha, P. Veeresha and Venkatesha, The Fischer-Marsden conjecture on non-Kenmotsu(k, μ)- almost Kenmotsu manifolds, J. Geom. (2019) 110:1.
[11] R. Prasad and V. Srivastava, On ε-Lorentzian Para-Sasakian manifolds, Commun. Korean Math. Soc. 27(2), (2012), 297-306.
[12] S. Sasaki, Lecture note on almost contact manifolds, Part-I, Tohoku University, 1965.
[13] A. A. Shaikh, and S. K. Hui, On Weakly weakly concircular symmetric Manifolds, Ann. Sti. Ale Univ., Al. I. CUZA, Din Iasi, LV,f.1(2009), 167-186.
[14] R. N. Singh and Shravan K. Pandey, On a Quarter-Symmetric Metric Connection in an LP-Sasakian Manifold, Thai Journal of Mathematics, Volume 12(2014) Number 2: 357-371.
[15] T. Takahashi, Sasakian --symmetric spaces, Tohoku Math. J. 29 (1977), 91-113.
[16] Venkatesha, K. T. Pradeep Kumar, C. S. Bagewadi and Gurupadavva Ingalahalli, On concircular Φ-recurrent K-contact manifold admitting semi-symmetric metric connection, International Journal of Mathematics and Mathematical Sciences, Hindawi Publishing Corporation, Volume 2012, Article ID 757032,
[17] Venkatesha, K. T. Pradeep Kumar and C. S. Bagewadi, On Quarter-Symmetric Metric Connection in a Lorentzian Para-Sasakian Manifold, Azerbaijan Journal of Mathematic,s 5(1), (2015), 3-12.
[18] Venkatesha, Arasaiah, S. V. Vishnuvardhana, R. T. Naveen Kumar, Some Symmetric Properties of Kenmotsu Manifolds admitting Semi-Symmetric Metric Connection, FACTA UNIVERSITATIS, Ser. Math. Inform. 34(1), (2019), 35-44.
[19] Venkatesha and S. V. Vishnuvardhana,(ε)-Kenmotsu maniolds admitting a Semi-Symmetric Metric Connection, Italian Jouranl of Pure and Applied Mathematics, 38, (2017), 615-623.
[20] Venkatesha, C. S. Bagewadi, and K. T. Pradeep Kumar, Some results on Lorentzianpara-Sasakian manifolds, ISRN Geometry, vol. 2011, Article ID 161523, 9 pages, 2011. doi:10.5402/2011/161523.
[21] Venkatesha, K. T. Pradeep Kumar, C. S. Bagewadi and Gurupadavva Ingalahalli, On concircular Φ-recurrent K-contact manifold admitting semi-symmetric metric connection, International Journal of Mathematics and Mathematical Sciences, Hindawi Publishing Corporation, Volume 2012, Article ID 757032, 9 pages doi:10.1155/2012/757032.
[22] S. V. Vishnuvardhana and Venkatesha, Results on para-Sasakian manifold admitting a quarter symmetric metric connection, CUBO, A Mathematical Journal, 22(2), (2020), 257-271.
[23] T. J. Willmore, An introduction to differential geometry, Oxford Univ. Press, 1959.
[24] K. Yano, On semi-symmetric metric connections, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579-1586.
[25] A. Yildiz and C. Murathan, On Lorentizian α-Sasakian manifolds, Kyungpook Math. J., 45, (2005), 95-103.
[26] A. Yildiz and U. C. De, On a type of Kenmotsu manifolds, Differential Geometry-Dynamical Systems, 12, (2010), 289-298.
B. M. Roopa, K. T. Pradeep Kumar, K. H. Arun Kumar, Govardhana Reddy H G, "Concircular -Symmetric ()-Lorentzian Para-Sasakian Manifold Admitting Quarter-Symmetric Metric Connection," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 7, pp. 52-57, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I7P508