On a Type of Semi-Symmetric Non-Metric Connection in HSU-Unified Structure Manifold

Year 2021, , 383 - 390, 29.10.2021

Shivani Sundriyal , Jaya Upreti

https://doi.org/10.36890/iejg.980796

Abstract

In the present paper, we have studied some properties of a semi-symmetric non-metric connection in HSU-unified structure manifold and HSU-Kahler manifold. Some new results on such manifolds have been obtained.

Keywords

Semi-symmetric non-metric connection, Levi-Civita connection, HSU-unified structure manifold, HSU-Kahler manifold, Nijenhuis tensor

References

• [1] Agashe, N.S.: A semi-symmetric non-metric connection on a Riemannian manifold. Indian J. pure appl. Math. 23, 399-409 (1992).
• [2] Andonie, OC., Smaranda, D.: Certaines connexions semisymetriques. Tensor. 31, 8-12 (1977).
• [3] Chaubey, S. K., Ojha, R.H.: On a semi-symmetric non-metric and quarter symmetric metric connexions. Tensor N.S. 70 (2), 202-203 (2008).
• [4] Chaubey, S. K., Ojha, R.H.: On a semi-symmetric non-metric connection. Filomat. 26 (2), 269-275 (2012).
• [5] Chaubey, S. K., Yildiz, A.: Riemannian manifolds admitting a new type of semisymmetric nonmetric connection. Turkish Journal of Mathematics. 43 (4), 1887-1904 (2019).
• [6] Hyden, A.: Sub-Spaces of a Space with Torsion. Proceedings of London Mathematical Society. 2 (1), 27-50 (1932).
• [7] Kobayashi, S., Nomizu, K.: Foundation of differential geometry, Vol. I and II. Interscience Publisher, London (1969).
• [8] Kumar, S., Kandpal, D., Upreti, J.: On a HSU-unified Structure Manifold with a Recurrent Metric Connection. Journal of Computer and Mathematical Sciences. 8 (8), 366-372 (2017).
• [9] Kumar, S., Upreti, J.: A new connection in an almost para-contact manifold. Journal of National Academy of Mathematics, Gorakhpur. 28, 42-52 (2014).
• [10] MIshra, R.S.: Structures on a differentiable manifold and their applications. Chandrama Prakashan, 50-A Balrampur Hause, Allahabad, India (1984).
• [11] Nivas, R., Agnihotri, A.: On HSU-unified Structure Manifold with a Quarter-symmetric Non-metric Connection. Bulletin of Mathematical Sciences and Applications. 3, 63-70 (2013).
• [12] Sengupta, J., De, U.C, Binh, T.: On a type of semi-symmetric non-metric connection on a Riemannian manifold. Indian Journal of Pure and Applied Mathematics. 31 (12) 1659-1670 (2000).
• [13] Yano, K.: On semi-symmetric metric connections. Revue Roumaine de Mathematiques Pures et Appliquees. 15 1579-1586 (1970).