Honam Mathematical Journal (호남수학학술지)

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ON A PRODUCT-SYMMETRIC RECURRENT-METRIC CONNECTION IN AN ALMOST HERMITIAN MANIFOLD

  • Kim, Jaeman (Department of Mathematics Education, Kangwon National University)
  • Received : 2013.02.07
  • Accepted : 2013.03.18
  • Published : 2013.06.25
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Abstract

In the present paper, we define a product-symmetric recurrent-metric connection in an almost Hermitian manifold and study some properties of this connection, in particular, its curvature properties.

Keywords

Acknowledgement

Supported by : Kangwon National University

References

  1. Besse, A.L., Einstein Manifolds, Springer, Berlin, 1987.
  2. Chaubey, S.K., Dubey, A.K. and Ojha, R.H., Some properties of quarter-symmetric non-metric connection in a Kahler manifold, Int. J. Contemp. Math. Sciences 5 (2010), 1001-1007.
  3. Chaubey, S.K. and Ojha, R.H., On quarter-symmetric non-metric connection on an almost Hermitian manifold, Bull. Math. Anal. Appl. 2 (2010), 77-83.
  4. De, U.C., On a type of semi-symmetric connection on a Riemannian manifold, Indian J. Pure Appl. Math. 21 (1990), 334-338.
  5. De, U.C., On a type of semi-symmetric metric connection on a Riemannian manifold, Analete Stiintifice Ale Universitatii, AL.I.CUZA DIN IASI, Math., Tomul XXXVIII, Fasc. 1 (1991), 105-108.
  6. De, U.C. and Sengupta, J., On Quarter-symmetric metric connection on a Sasakian manifold, Commun. Fac. Sci. Univ. Ank. Ser. Al Math. Stat. 49 (2000), 7-13.
  7. Friedmann, A. and Schouten, J.A., Uber die Geometrie der halbsymmetrischen ubertragungen, Math. Z. 21 (1924), 211-223. https://doi.org/10.1007/BF01187468
  8. Golab, S., On semi-symmetric and quarter symmetric linear connections, Tensor, N.S. 29 (1975), 249-254.
  9. Hayden, H.A., Subspaces of a space with torsion, Proc. London Math. Soc. 34 (1932), 27-50.
  10. Mishra, R.S. and Pandey, S.N., Semi-symmetric metric connection in an almost contact manifold, Indian J. Pure Appl. Math. 9 (1978), 570-580.
  11. Mishra, R.S. and Pandey, S.N., On quarter-symmetric metric F-connections, Tensor, N.S. 34 (1980), 1-7.
  12. Mondal, A.K. and De, U.C., Some properties of a quarter-symmetric metric connection on a Sasakian manifold, Bull. Math. Anal. Appl. 1 (2009), 99-108.
  13. Mukhopadhyay, S., Roy, A.K. and Barua, B., Some properties of a quarter-symmetric metric connection on a Riemannian manifold, Soochow J. of Math. 17 (1991), 205-211.
  14. Ojha, R.H. and Prasad, S., Semi-symmetric metric s-connection in a Sasakian manifold, Indian J. Pure Appl. Math. 16 (1985), 341-344.
  15. Rastogi, S.C., On quarter-symmetric metric connection, C.R. Acad. Bulg. Sci. 31 (1978), 811-814.
  16. Rastogi, S.C., On quarter-symmetric metric connections, Tensor, N.S. 44 (1987), 133-141.
  17. Rastogi, S.C., A note on quarter-symmetric metric connections, Indian J. Pure Appl. Math. 18 (1987), 1107-1112.
  18. Sengupta, J. and Biswas, B., Quarter-symmetric non-metric connection on a Sasakian manifold, Bull. Cal. Math. Soc. 95 (2003), 169-176.
  19. Yano, K., On semi-symmetric metric connection, Rev. Roum. Math. Pures et Appl. 15 (1970), 1579-1586.
  20. Yano, K. and Imai, T., On semi-symmetric metric ${\phi}$-connections in a Sasakian manifold, Kodai Math. Sem. Rep. 28 (1977), 150-158. https://doi.org/10.2996/kmj/1138847436
  21. Yano, K. and Imai, T., Quarter-symmetric metric connections and their curvature tensors, Tensor, N.S. 38 (1982), 13-18.