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E-BOCHNER CURVATURE TENSOR ON ( κ , µ)-CONTACT METRIC MANIFOLDS

Year 2014, Volume: 7 Issue: 1, 143 - 153, 30.04.2014
https://doi.org/10.36890/iejg.594505

Abstract

References

  • [1] Arslan, K., Ezentas, R., Mihai, I., Murthan, C. and O¨ zgu¨r, C., Certain inequalities for submanifolds in (κ, µ)-contact space forms, Bull. Austral. Soc., 64(2001), 201-212.
  • [2] Blair, D.E, Contact manifolds in Reimannian geometry, Lecture notes in Math., 509, Springer-verlag., 1976.
  • [3] Blair, D.E, Koufogiorgos T. and Papantoniou B.J., Contact metric manifold satisfying a nullity condition, Israel J.Math. 91(1995), 189-214.
  • [4] Blair, D.E, Two remarks on contact metric structures, Tohoku Math. J. 29(1977), 319-324.
  • [5] Bochner, S., Curvature and Betti number, Ann. of Math., 50(1949), 77-93 .
  • [6] Boeckx, E., A full classificstion of contact metric (κ, µ)-spaces, Illinois J.Math. 44(2000), 212-219 .
  • [7] Boothby, W.M. and Wang, H.C.,On contact manifolds, Annals of Math., 68(1958), 721-734 .
  • [8] De, U.C and Sarkar, A., On Quasi-conformal curvature tensor of (κ, µ)-contact metric manifold, Math. Reports 14(64), (2012), 115-129.
  • [9] Endo, H., On K-contact Reimannian manifolds with vanishing E-contact Bochner curvature tensor, Colloq.Math. 62(1991), 293-297.
  • [10] Ghosh,S. and De, U.C, On a class of (κ, µ)-contact metric manifolds, Analele Universitˇatii Oradea Fasc. Mathematica, Tom. 19(2012), 231-242.
  • [11] Ghosh, S. and De, U.C., On φ-Quasiconformally symmetric (κ, µ)-contact metric manifolds, Lobachevskii Journal of Mathematics, 31(2010), 367-375.
  • [12] Jun, J.B., Yildiz, A. and De, U.C.,On φ-recurrent (κ, µ)-contact metric manifolds, Bull. Korean Math. Soc. 45(4), 689(2008).
  • [13] Kim, J.S, Tripathi, M.M. and Choi, J.D, On C-Bochner curvature tensor of a contact metric manifold, Bull. Korean Math. Soc. 42(2005), 713-724.
  • [14] Kowalski, O., An explicit classification of 3-dimensional Reimannian spaces satisfying R(X, Y ) · R = 0, Czecchoslovak Math. J. 46(121) (1996), 427-474.
  • [15] Matsumoto, M. and Chuman, G., On C-Bochner curvature tensor, TRU Math., 5(1969), 21-30.
  • [16] Özgür, C., Contact metric manifolds with cyclic-parallel Ricci tensor, Diff. Geom. Dynamical systems, 4(2000), 21-25.
  • [17] Papantoniou, B.J., Contact Remannian manifolds satisfying R(ξ, X) · R = 0 and ξ ∈ (κ, µ)- nullity distribution, Yokohama Math.J., 40(1993), 149-161.
  • [18] Szabo, Z.I., Structure theorems on Reimannian spaces satisfying R(X, Y ) · R = 0. I. The local version, J. Differential Geom. 17(1982), 531-582.
  • [19] Tanno, S., Ricci curvatures of contact Reimannian manifolds, Tˆˆohoku Math. J., 40(1988), 441-448.
  • [20] Yildiz, A., De, U.C, A classification of (κ, µ)-contact matric manifold, Commun. Korean Soc. 27(2012), 327-339.Soc. 27(2012), 327-339.
Year 2014, Volume: 7 Issue: 1, 143 - 153, 30.04.2014
https://doi.org/10.36890/iejg.594505

Abstract

References

  • [1] Arslan, K., Ezentas, R., Mihai, I., Murthan, C. and O¨ zgu¨r, C., Certain inequalities for submanifolds in (κ, µ)-contact space forms, Bull. Austral. Soc., 64(2001), 201-212.
  • [2] Blair, D.E, Contact manifolds in Reimannian geometry, Lecture notes in Math., 509, Springer-verlag., 1976.
  • [3] Blair, D.E, Koufogiorgos T. and Papantoniou B.J., Contact metric manifold satisfying a nullity condition, Israel J.Math. 91(1995), 189-214.
  • [4] Blair, D.E, Two remarks on contact metric structures, Tohoku Math. J. 29(1977), 319-324.
  • [5] Bochner, S., Curvature and Betti number, Ann. of Math., 50(1949), 77-93 .
  • [6] Boeckx, E., A full classificstion of contact metric (κ, µ)-spaces, Illinois J.Math. 44(2000), 212-219 .
  • [7] Boothby, W.M. and Wang, H.C.,On contact manifolds, Annals of Math., 68(1958), 721-734 .
  • [8] De, U.C and Sarkar, A., On Quasi-conformal curvature tensor of (κ, µ)-contact metric manifold, Math. Reports 14(64), (2012), 115-129.
  • [9] Endo, H., On K-contact Reimannian manifolds with vanishing E-contact Bochner curvature tensor, Colloq.Math. 62(1991), 293-297.
  • [10] Ghosh,S. and De, U.C, On a class of (κ, µ)-contact metric manifolds, Analele Universitˇatii Oradea Fasc. Mathematica, Tom. 19(2012), 231-242.
  • [11] Ghosh, S. and De, U.C., On φ-Quasiconformally symmetric (κ, µ)-contact metric manifolds, Lobachevskii Journal of Mathematics, 31(2010), 367-375.
  • [12] Jun, J.B., Yildiz, A. and De, U.C.,On φ-recurrent (κ, µ)-contact metric manifolds, Bull. Korean Math. Soc. 45(4), 689(2008).
  • [13] Kim, J.S, Tripathi, M.M. and Choi, J.D, On C-Bochner curvature tensor of a contact metric manifold, Bull. Korean Math. Soc. 42(2005), 713-724.
  • [14] Kowalski, O., An explicit classification of 3-dimensional Reimannian spaces satisfying R(X, Y ) · R = 0, Czecchoslovak Math. J. 46(121) (1996), 427-474.
  • [15] Matsumoto, M. and Chuman, G., On C-Bochner curvature tensor, TRU Math., 5(1969), 21-30.
  • [16] Özgür, C., Contact metric manifolds with cyclic-parallel Ricci tensor, Diff. Geom. Dynamical systems, 4(2000), 21-25.
  • [17] Papantoniou, B.J., Contact Remannian manifolds satisfying R(ξ, X) · R = 0 and ξ ∈ (κ, µ)- nullity distribution, Yokohama Math.J., 40(1993), 149-161.
  • [18] Szabo, Z.I., Structure theorems on Reimannian spaces satisfying R(X, Y ) · R = 0. I. The local version, J. Differential Geom. 17(1982), 531-582.
  • [19] Tanno, S., Ricci curvatures of contact Reimannian manifolds, Tˆˆohoku Math. J., 40(1988), 441-448.
  • [20] Yildiz, A., De, U.C, A classification of (κ, µ)-contact matric manifold, Commun. Korean Soc. 27(2012), 327-339.Soc. 27(2012), 327-339.
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Uday Chand De This is me

Srimayee Samuı This is me

Publication Date April 30, 2014
Published in Issue Year 2014 Volume: 7 Issue: 1

Cite

APA Chand De, U., & Samuı, S. (2014). E-BOCHNER CURVATURE TENSOR ON ( κ , µ)-CONTACT METRIC MANIFOLDS. International Electronic Journal of Geometry, 7(1), 143-153. https://doi.org/10.36890/iejg.594505
AMA Chand De U, Samuı S. E-BOCHNER CURVATURE TENSOR ON ( κ , µ)-CONTACT METRIC MANIFOLDS. Int. Electron. J. Geom. April 2014;7(1):143-153. doi:10.36890/iejg.594505
Chicago Chand De, Uday, and Srimayee Samuı. “E-BOCHNER CURVATURE TENSOR ON ( κ , )-CONTACT METRIC MANIFOLDS”. International Electronic Journal of Geometry 7, no. 1 (April 2014): 143-53. https://doi.org/10.36890/iejg.594505.
EndNote Chand De U, Samuı S (April 1, 2014) E-BOCHNER CURVATURE TENSOR ON ( κ , µ)-CONTACT METRIC MANIFOLDS. International Electronic Journal of Geometry 7 1 143–153.
IEEE U. Chand De and S. Samuı, “E-BOCHNER CURVATURE TENSOR ON ( κ , µ)-CONTACT METRIC MANIFOLDS”, Int. Electron. J. Geom., vol. 7, no. 1, pp. 143–153, 2014, doi: 10.36890/iejg.594505.
ISNAD Chand De, Uday - Samuı, Srimayee. “E-BOCHNER CURVATURE TENSOR ON ( κ , )-CONTACT METRIC MANIFOLDS”. International Electronic Journal of Geometry 7/1 (April 2014), 143-153. https://doi.org/10.36890/iejg.594505.
JAMA Chand De U, Samuı S. E-BOCHNER CURVATURE TENSOR ON ( κ , µ)-CONTACT METRIC MANIFOLDS. Int. Electron. J. Geom. 2014;7:143–153.
MLA Chand De, Uday and Srimayee Samuı. “E-BOCHNER CURVATURE TENSOR ON ( κ , )-CONTACT METRIC MANIFOLDS”. International Electronic Journal of Geometry, vol. 7, no. 1, 2014, pp. 143-5, doi:10.36890/iejg.594505.
Vancouver Chand De U, Samuı S. E-BOCHNER CURVATURE TENSOR ON ( κ , µ)-CONTACT METRIC MANIFOLDS. Int. Electron. J. Geom. 2014;7(1):143-5.