Research Article
BibTex RIS Cite

PROJECTIVE CURVATURE TENSOR OF A SEMI-SYMMETRIC METRIC CONNECTION IN A KENMOTSU MANIFOLD

Year 2013, Volume: 6 Issue: 1, 159 - 169, 30.04.2013

Abstract



References

  • [1] Amur, K. and Pujar, S.S., On submanifolds of a Riemannian manifold admitting a metric semi-symmetric connection, Tensor, N.S., 32(1978), 35-38.
  • [2] Arslan, K., Murathan, C. and O¨zgu¨r, C., On φ-conformally flat contact metric manifolds, Balkan J. Geom. Appl. (BJGA), 5(2)(2000), 1-7.
  • [3] Binh, T.Q., On semi-symmetric connection, Periodica Math. Hungerica, 21(2), 1990, 101-107.
  • [4] Blair, D.E., Contact manifolds in Riemannian geometry, Lecture Note in Mathematics, 509, Springer-Verlag Berlin, 1976.
  • [5] Cabrerizo, J.L., Fernandez, M., Fernandez, L.M. and Zhen, G. : On ξ-conformaly flat K- contact manifolds, Indian J. Pure and Applied Math., 28(1997), 725-734.
  • [6] Chaubey, S.K. and Ojha, R.H., On a semi-symmetric non-metric connection, Filomat 25:4 (2011), 19-27.
  • [7] Chaubey, S.K. and Ojha, R.H., On a semi-symmetric non-metric connection, Filmot 26:2 (2012), 63-69.
  • [8] De, U.C. and Biswas, S.C., On a type of semi-symmetric metric connection on a Riemannian manifold, Pub. De L Institut Math., N.S., Tome 61(75), 1997, 90-96.
  • [9] De, U.C. and Pathak, G., On 3-dimensional Kenmotsu manifolds, Indian J. Pure Applied Math., 35 (2004), 159-165.
  • [10] Friedmann, A. and Schouten, J.A., U¨ ber die Geometric der halbsymmetrischen U¨ bertragung, Math., Zeitschr., 21(1924), 211-223.
  • [11] Hayden, H.A., Subspaces of space with torsion, Proc. London Math. Soc., 34(1932), 27-50.
  • [12] Ianus, S. and Smaranda, D., Some remarkable structures on the product of an almost contact metric manifold with the real line, Papers from the National Coll. on Geometry and Topology, Univ. Timisoara, (1997),107-110.
  • [13] Jun, J.B. , De, U.C. and Pathak, G., On Kenmotsu manifolds, J. Korean Math. Soc., 42(2005), 435-445.
  • [14] Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24(1972), 93-103.
  • [15] Oubina, A., New classes of contact metric structures, Publ. Math. Debrecen, 32(3- 4)(1985),187-193.
  • [16] O¨zgu¨r, C. and De, U.C., On the quasi-conformal curvature tensor of a Kenmotsu manifold, Mathematica Pannonica, 17/2, (2006), 221-228.
  • [17] Prvanovic´, M., On pseudo metric semi-symmetric connections, Pub. De L Institut Math., Nouvelle serie, 18 (32), 1975, 157-164.
  • [18] Sharfuddin, A. and Hussain, S.I., Semi-symmetric metric connexions in almost contact man- ifolds, Tensor, N.S., 30(1976), 133-139.
  • [19] Tanno, S., The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. j., 21(1969), 21-38.
  • [20] Yano, K., On semi-symmetric connection, Revue Roumaine de Math. Pure et Appliques, 15(1970), 1570-1586.
  • [21] Yano, K. and Bochner, S., Curvature and Betti numbers, Annals of Mathematics studies, 32(Princeton university press) (1953).
  • [22] Yıldiz, A., De, U.C. and Acet, B.E., On Kenmotsu manifolds satisfying certain curvature conditions, SUT J. of Math. 45, 2(2009), 89-101.
  • [23] Yılmaz, H.B., On weakly symmetric manifolds with a type of semi-symmetric non-metric connection, Annales Polonici Mathematici 102.3 (2011).
  • [24] Zhen, G., On conformal symmetric K-contact manifolds, Chinese Quart. J. Math., 7(1992), 5-10.
  • [25] Zhen, G., Cabrerizo, J. L., Fernandez, L. M. and Fernandez, M., The structure of a class of K-contact manifolds, Acta Math. Hungar, 82(4)(1999), 331-340.
  • [26] Zengin F. O., Uysal S. A. and Demirbag S. A., On sectional curvature of a Riemannian manifold with semi-symmetric metric connection, Ann. Polon. Math. 101(2011), 131-138.
Year 2013, Volume: 6 Issue: 1, 159 - 169, 30.04.2013

Abstract

References

  • [1] Amur, K. and Pujar, S.S., On submanifolds of a Riemannian manifold admitting a metric semi-symmetric connection, Tensor, N.S., 32(1978), 35-38.
  • [2] Arslan, K., Murathan, C. and O¨zgu¨r, C., On φ-conformally flat contact metric manifolds, Balkan J. Geom. Appl. (BJGA), 5(2)(2000), 1-7.
  • [3] Binh, T.Q., On semi-symmetric connection, Periodica Math. Hungerica, 21(2), 1990, 101-107.
  • [4] Blair, D.E., Contact manifolds in Riemannian geometry, Lecture Note in Mathematics, 509, Springer-Verlag Berlin, 1976.
  • [5] Cabrerizo, J.L., Fernandez, M., Fernandez, L.M. and Zhen, G. : On ξ-conformaly flat K- contact manifolds, Indian J. Pure and Applied Math., 28(1997), 725-734.
  • [6] Chaubey, S.K. and Ojha, R.H., On a semi-symmetric non-metric connection, Filomat 25:4 (2011), 19-27.
  • [7] Chaubey, S.K. and Ojha, R.H., On a semi-symmetric non-metric connection, Filmot 26:2 (2012), 63-69.
  • [8] De, U.C. and Biswas, S.C., On a type of semi-symmetric metric connection on a Riemannian manifold, Pub. De L Institut Math., N.S., Tome 61(75), 1997, 90-96.
  • [9] De, U.C. and Pathak, G., On 3-dimensional Kenmotsu manifolds, Indian J. Pure Applied Math., 35 (2004), 159-165.
  • [10] Friedmann, A. and Schouten, J.A., U¨ ber die Geometric der halbsymmetrischen U¨ bertragung, Math., Zeitschr., 21(1924), 211-223.
  • [11] Hayden, H.A., Subspaces of space with torsion, Proc. London Math. Soc., 34(1932), 27-50.
  • [12] Ianus, S. and Smaranda, D., Some remarkable structures on the product of an almost contact metric manifold with the real line, Papers from the National Coll. on Geometry and Topology, Univ. Timisoara, (1997),107-110.
  • [13] Jun, J.B. , De, U.C. and Pathak, G., On Kenmotsu manifolds, J. Korean Math. Soc., 42(2005), 435-445.
  • [14] Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24(1972), 93-103.
  • [15] Oubina, A., New classes of contact metric structures, Publ. Math. Debrecen, 32(3- 4)(1985),187-193.
  • [16] O¨zgu¨r, C. and De, U.C., On the quasi-conformal curvature tensor of a Kenmotsu manifold, Mathematica Pannonica, 17/2, (2006), 221-228.
  • [17] Prvanovic´, M., On pseudo metric semi-symmetric connections, Pub. De L Institut Math., Nouvelle serie, 18 (32), 1975, 157-164.
  • [18] Sharfuddin, A. and Hussain, S.I., Semi-symmetric metric connexions in almost contact man- ifolds, Tensor, N.S., 30(1976), 133-139.
  • [19] Tanno, S., The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. j., 21(1969), 21-38.
  • [20] Yano, K., On semi-symmetric connection, Revue Roumaine de Math. Pure et Appliques, 15(1970), 1570-1586.
  • [21] Yano, K. and Bochner, S., Curvature and Betti numbers, Annals of Mathematics studies, 32(Princeton university press) (1953).
  • [22] Yıldiz, A., De, U.C. and Acet, B.E., On Kenmotsu manifolds satisfying certain curvature conditions, SUT J. of Math. 45, 2(2009), 89-101.
  • [23] Yılmaz, H.B., On weakly symmetric manifolds with a type of semi-symmetric non-metric connection, Annales Polonici Mathematici 102.3 (2011).
  • [24] Zhen, G., On conformal symmetric K-contact manifolds, Chinese Quart. J. Math., 7(1992), 5-10.
  • [25] Zhen, G., Cabrerizo, J. L., Fernandez, L. M. and Fernandez, M., The structure of a class of K-contact manifolds, Acta Math. Hungar, 82(4)(1999), 331-340.
  • [26] Zengin F. O., Uysal S. A. and Demirbag S. A., On sectional curvature of a Riemannian manifold with semi-symmetric metric connection, Ann. Polon. Math. 101(2011), 131-138.
There are 26 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Ajit Barman

U. C. De

Publication Date April 30, 2013
Published in Issue Year 2013 Volume: 6 Issue: 1

Cite

APA Barman, A., & De, U. C. (2013). PROJECTIVE CURVATURE TENSOR OF A SEMI-SYMMETRIC METRIC CONNECTION IN A KENMOTSU MANIFOLD. International Electronic Journal of Geometry, 6(1), 159-169.
AMA Barman A, De UC. PROJECTIVE CURVATURE TENSOR OF A SEMI-SYMMETRIC METRIC CONNECTION IN A KENMOTSU MANIFOLD. Int. Electron. J. Geom. April 2013;6(1):159-169.
Chicago Barman, Ajit, and U. C. De. “PROJECTIVE CURVATURE TENSOR OF A SEMI-SYMMETRIC METRIC CONNECTION IN A KENMOTSU MANIFOLD”. International Electronic Journal of Geometry 6, no. 1 (April 2013): 159-69.
EndNote Barman A, De UC (April 1, 2013) PROJECTIVE CURVATURE TENSOR OF A SEMI-SYMMETRIC METRIC CONNECTION IN A KENMOTSU MANIFOLD. International Electronic Journal of Geometry 6 1 159–169.
IEEE A. Barman and U. C. De, “PROJECTIVE CURVATURE TENSOR OF A SEMI-SYMMETRIC METRIC CONNECTION IN A KENMOTSU MANIFOLD”, Int. Electron. J. Geom., vol. 6, no. 1, pp. 159–169, 2013.
ISNAD Barman, Ajit - De, U. C. “PROJECTIVE CURVATURE TENSOR OF A SEMI-SYMMETRIC METRIC CONNECTION IN A KENMOTSU MANIFOLD”. International Electronic Journal of Geometry 6/1 (April 2013), 159-169.
JAMA Barman A, De UC. PROJECTIVE CURVATURE TENSOR OF A SEMI-SYMMETRIC METRIC CONNECTION IN A KENMOTSU MANIFOLD. Int. Electron. J. Geom. 2013;6:159–169.
MLA Barman, Ajit and U. C. De. “PROJECTIVE CURVATURE TENSOR OF A SEMI-SYMMETRIC METRIC CONNECTION IN A KENMOTSU MANIFOLD”. International Electronic Journal of Geometry, vol. 6, no. 1, 2013, pp. 159-6.
Vancouver Barman A, De UC. PROJECTIVE CURVATURE TENSOR OF A SEMI-SYMMETRIC METRIC CONNECTION IN A KENMOTSU MANIFOLD. Int. Electron. J. Geom. 2013;6(1):159-6.