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

• Journal title : Honam Mathematical Journal
• Volume 35, Issue 2,  2013, pp.119-128
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2013.35.2.119
Title & Authors
ON A PRODUCT-SYMMETRIC RECURRENT-METRIC CONNECTION IN AN ALMOST HERMITIAN MANIFOLD
Kim, Jaeman;

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
product-symmetric recurrent-metric connection;almost Hermitian manifolds;Hermitian;almost K$\small{\ddot{a}}$hler;Einstein;double-recurrent 1-form;concurrent vector field;
Language
English
Cited by
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.

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.

21.
Yano, K. and Imai, T., Quarter-symmetric metric connections and their curvature tensors, Tensor, N.S. 38 (1982), 13-18.