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GEOMETRY OF A SEMI-SYMMETRIC RECURRENT METRIC CONNECTION

  • Jaeman Kim (Department of Mathematics Education Kangwon National University)
  • Received : 2023.02.02
  • Accepted : 2023.04.26
  • Published : 2023.10.31

Abstract

In the present paper, we study a semi-symmetric recurrent metric connection and verify its various geometric properties.

Keywords

Acknowledgement

The author would like to express his sincere thanks to the referee for valuable suggestions towards the improvement of this paper.

References

  1. N. S. Agashe and M. R. Chafle, A semi-symmetric nonmetric connection on a Riemannian manifold, Indian J. Pure Appl. Math. 23 (1992), no. 6, 399-409. 
  2. S. K. Chaubey, On semi-symmetric non-metric connection, Prog. of Math. 41-42 (2007), 11-20. 
  3. S. K. Chaubey and R. H. Ojha, On a semi-symmetric non-metric and quarter symmetric metric connections, Tensor (N.S.) 70 (2008), no. 2, 202-213. 
  4. U. C. De and S. Bandyopadhyay, On weakly symmetric Riemannian spaces, Publ. Math. Debrecen 54 (1999), no. 3-4, 377-381. https://doi.org/10.5486/pmd.1999.1999 
  5. L. P. Eisenhart, Riemannian Geometry, Princeton Univ. Press, Princeton, NJ, 1949. 
  6. J. P. Jaiswal and R. H. Ojha, Some properties of K-contact Riemannian manifolds admitting a semi-symmetric non-metric connection, Filomat 24 (2010), no. 4, 9-16.  https://doi.org/10.2298/FIL1004009J
  7. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry. Vol I, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York, 1963. 
  8. J. Sengupta, U. C. De, and T. Q. Binh, On a type of semi-symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math. 31 (2000), no. 12, 1659-1670. 
  9. Z. Szabo, Structure theorems on Riemannian spaces satisfying R(X, Y ).R = 0. I. The local version, J. Differential Geometry 17 (1982), no. 4, 531-582 (1983). http://projecteuclid.org/euclid.jdg/1214437486 
  10. Z. Szabo, Structure theorems on Riemannian spaces satisfying R(X, Y ).R = 0. II. Global versions, Geom. Dedicata 19 (1985), no. 1, 65-108. https://doi.org/10.1007/BF00233102 
  11. L. Tamassy and T. Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, in Differential geometry and its applications (Eger, 1989), 663-670, Colloq. Math. Soc. Janos Bolyai, 56, North-Holland, Amsterdam, 1992. 
  12. M. M. Tripathi, A new connection in a Riemannian manifold, Int. Electron. J. Geom. 1 (2008), no. 1, 15-24. 
  13. K. Yano, On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579-1586. 
  14. D. Zhao, T. Y. Ho, and A. J. Hyon, Geometries for a mutual connection of semi-symmetric metric recurrent connections, Filomat 34 (2020), no. 13, 4367-4374. https://doi.org/10.2298/FIL2013367Z