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The objective of the present paper is to study the relation between the Levi-Civita connection and the quarter-symmetric metric connection in a para-Sasakian manifold. Next, we study ξ-W˜7-flat, ˜ W7

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INGALAHALLI, G., ANIL, S. C., & BAGEWADI, C. S. (2021). A STUDY ON W7-CURVATURE TENSOR IN PARA-SASAKIAN MANIFOLD ADMITTING QUARTER-SYMMETRIC METRIC CONNECTION. Asian Journal of Mathematics and Computer Research, 28(1), 17-25. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/6237
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Kaneyuki S, Williams F. Almost paracontact and parahodge structures on manifolds. Nagoya Math. J. 1985;99:173-187.

Zamkovoy S. Canonical connections on paracontact manifolds. Ann. Glob. Anal. Geom. 2009;36:37-60.

Adati T, Matsumoto K. On conformally recurrent and conformally symmetric P-Sasakian manifolds. TRU Math. 1977;17:25-32.

Biswas SC, De UC. Quarter-symmetric metric connection in an SP-Sasakian manifold. Commun. Fac. Sci. Univ. Ank. Series. 1997;46:49-56.

Hui SK, Chakraborty D. Para-Sasakian Manifolds and Ricci Solitons. Ilirias Journal of Mathematics. 2017;6 (1):25-34.

Hui SK. On ϕ-pseudo symmetric Para-Sasakian manifolds. Acta Univ. Apulensis. 2014;39:161- 178.

Prakasha DG, Hadimani BS. η-Ricci solitons on para-Sasakian manifolds. J. Geom. 2017;108:383-392.

Shukla SS, Mukesh Kumar Shukla. On ϕ-Symmetric Para-Sasakian Manifolds. Int. Journal of Math. Analysis. 2010;4:761-769.

Tripathi MM, Kili¸c E, Perkta¸s SY, Kele¸s S. Indefinite almost paracontact metric manifolds. International Journal of Mathematics and Mathematical Sciences. 2010;2010:1-19.

Golab S. On Semi-symmetric and Quarter-symmetric linear connections. Tensor NS. 1975;29:293-301.

Mishra RS, Pandey SN. On Quarter-symmetric metric F-connections. Tensor N.S. 1980;34:1-7.

Yano K, Imai T. Quarter-symmetric metric connections and their curvature tensors. Tensor NS. 1982;38:13-18.

Rastogi SC. On Quarter-symmetric metric connections. Tensor NS. 1987;44 (2):133-141.

Mukhopadhyay S, Roy AK, Barua B. Some properties of quarter symmetric metric connection on a Riemannian manifold. Soochow J. Math. 1991;17 (2):205-211.

Abul Kalam Mondal, De UC. Some Properties of a Quarter-Symmetric Metric Connection on a Sasakian Manifold. Bulletin of Mathematical Analysis and Applications. 2009;1 (3):99-108.

Tripathi MM. A new connection in a Riemannian manifold. 5 Feb 2008; arXiv:0802.0569v1.

Shaikh AA, Jana SK. Quarter symmetric metric connection on a (k, µ)-contact metric manifold. Commun. Fac. Sci. Univ. Ank. Series A1. 2006;55:33-45.

Bagewadi CS, Gurupadavva Ingalahalli. A Study on the ϕ-Symmetric K-Contact Manifold admitting Quarter-Symmetric Metric Connection. Journal of Mathematical Physics, Analysis, Geometry. 2014;10 (4):399-411.

Gurupadavva Ingalahalli, Bagewadi CS. A Study on Conservative C-Bochner Curvature Tensor in K-Contact and Kenmotsu Manifolds Admitting Semisymmetric Metric Connection. ISRN Geometry. 2012;(2012): 1-14.

Gurupadavva Ingalahalli, Bagewadi CS. On ϕ-Symmetry of C-Bochner Curvature Tensor in Para-Sasakian manifold admitting Quarter-Symmetric metric monnection. Asian Journal of Mathematics and Computer Research. 2017;17 (3):172-183.

Pradeep Kumar KT, Venkatesha, Bagewadi CS. On ϕ-Recurrent Para-Sasakian Manifold Admitting Quarter-Symmetric Metric Connection. 2012;(2012):1-10.

Hui SK. On ϕ-pseudo symmetric Kenmotsu manifolds with respect to quarter-symmetric metric connection. Applied Sciences. 2013;15:30-36.

Tripathi MM, Punam Gupta. τ -curvature tensor on a semi-reimannian manifold. J. Adv. Math. Studies. 2011;4 (1):117-129.

Moindi SK. A Study of W7-Curvature Tensor in LP-Sasakian Manifold. International Journal on Future Revolution in Computer Science Communication Engineering. 2017;3 (10):102-105.

Shyam Kishor, Pushpendra Verma. On W7-curvature tensor of Generalized Sasakian-Space Forms. International Journal of Mathematics Trends and Technology (IJMTT). 2017;49 (2):100-112.

Friedmann A, Schouten JA. Uber die Geometrie der halbsymmetrischen Ubertragung. Math. Zeitschr. 1924;21:211-223.

Takahashi T. Sasakian ϕ-symmetric spaces. Tohoku Math. J. 1977;29:91-113.