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Year 2017, Volume: 5 Issue: 1, 9 - 18, 30.04.2017
https://doi.org/10.36753/mathenot.421477

Abstract

References

  • [1] Blair, D.E., Koufogiorgos T. and Papantoniou B. J., Contact metric manifold satisfying a nullity condition, Israel J.Math., 91(1995), 189 − 214.
  • [2] Blair, D. E., Kim, J. S. and Tripathi, M. M.,On the concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc., 42(2005), 883-892.
  • [3] Blair, D.E, Two remarks on contact metric structures, Tohoku Math. J., 29(1977), 319 − 324.
  • [4] Boothby, W. M. and Wang, H. C., On contact manifolds, Ann of Math., 68(1958), 721 − 734.
  • [5] De, U.C and Sarkar, A., On Quasi-conformal curvature tensor of (k, µ)-contact metric manifold, Math. Reports, 14(64), 2(2012), 115 − 129.
  • [6] Ghosh, S. and De, U. C., On φ-Quasiconformally symmetric (k, µ)-contact metric manifolds, Lobachevskii Journal of Mathematics, 31(2010), 367 − 375.
  • [7] Jun, J.B., Yildiz, A. and De, U.C.,On φ-recurrent (k, µ)-contact metric manifolds, Bull. Korean Math. Soc. 45(4)(2008), 689.
  • [8] Jeong, J. C., Lee, J. D., Oh, G. H. and Pak, J. S., A note on the contact conformal curvature tensor, Bull. Korean Math. Soc., 27(1990), 133 − 142.
  • [9] Kang, T. H. and Pak, J. S., Some remarks for th spectrum of the p-Laplacian on Sasakian manifolds, J. Korean Math. Soc., 32(1995), 341 − 350.
  • [10] Kim, J. S., Choi, J., Özgür, C. and Tripathi, M. M.,On the Contact conformal curvature tensor of a contact metric manifold, Indian J. pure appl. Math., 37(4)(2006), 199 − 206.
  • [11] Kitahara, H., Matsuo, K. and Pak, J. S., A conformal curvature tensor field on Hermitian manifolds, J. Korean Math. Soc., 27(1990), 27 − 30.
  • [12] Kuhnel, W., Conformal transformations between Einstein spaces, Conformal geometry (Bonn, 1985/1986), 105-146, Asepects math., E12, Vieweg, Braunschweig, 1988.
  • [13] Papantoniou, B.J., Contact Riemannian manifolds satisfying R(ξ, X) · R = 0 and ξ ∈ (k, µ)-nullity distribution, Yokohama Math.J., 40(1993), 149 − 161.
  • [14] Pak, J. S., Jeong, J. C. and Kim, W. T., The contact conformal curvature tensor field and the spectrum of the Laplacian, J. Korean. Math. Soc., 28(1991), 267 − 274.
  • [15] Pak, J. S. and Shin, Y. J., A note on contact conformal curvature tensor, Commun. Korean Math. Soc., 13(2)(1998), 337 − 343.
  • [16] Tanno, S., Ricci curvatures of contact Riemannian manifolds, Tôhoku Math. J., 40(1988), 441 − 448 .
  • [17] Yano, K., Concircular geometry I. concircular transformations, Proc. Imp. Acad. Tokyo, 16(1940), 195-200.
  • [18] Yildiz, A. and De, U. C., A classification of (k, µ)-contact metric manifolds, Commun. Korean Math. Soc., 27(2012), 327-339.

On a Subclass of (k, µ)-Contact Metric Manifolds

Year 2017, Volume: 5 Issue: 1, 9 - 18, 30.04.2017
https://doi.org/10.36753/mathenot.421477

Abstract

The object of this paper is to characterize (k, µ)-contact metric manifolds satisfying certain curvature
conditions on the contact conformal curvature tensor. 

References

  • [1] Blair, D.E., Koufogiorgos T. and Papantoniou B. J., Contact metric manifold satisfying a nullity condition, Israel J.Math., 91(1995), 189 − 214.
  • [2] Blair, D. E., Kim, J. S. and Tripathi, M. M.,On the concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc., 42(2005), 883-892.
  • [3] Blair, D.E, Two remarks on contact metric structures, Tohoku Math. J., 29(1977), 319 − 324.
  • [4] Boothby, W. M. and Wang, H. C., On contact manifolds, Ann of Math., 68(1958), 721 − 734.
  • [5] De, U.C and Sarkar, A., On Quasi-conformal curvature tensor of (k, µ)-contact metric manifold, Math. Reports, 14(64), 2(2012), 115 − 129.
  • [6] Ghosh, S. and De, U. C., On φ-Quasiconformally symmetric (k, µ)-contact metric manifolds, Lobachevskii Journal of Mathematics, 31(2010), 367 − 375.
  • [7] Jun, J.B., Yildiz, A. and De, U.C.,On φ-recurrent (k, µ)-contact metric manifolds, Bull. Korean Math. Soc. 45(4)(2008), 689.
  • [8] Jeong, J. C., Lee, J. D., Oh, G. H. and Pak, J. S., A note on the contact conformal curvature tensor, Bull. Korean Math. Soc., 27(1990), 133 − 142.
  • [9] Kang, T. H. and Pak, J. S., Some remarks for th spectrum of the p-Laplacian on Sasakian manifolds, J. Korean Math. Soc., 32(1995), 341 − 350.
  • [10] Kim, J. S., Choi, J., Özgür, C. and Tripathi, M. M.,On the Contact conformal curvature tensor of a contact metric manifold, Indian J. pure appl. Math., 37(4)(2006), 199 − 206.
  • [11] Kitahara, H., Matsuo, K. and Pak, J. S., A conformal curvature tensor field on Hermitian manifolds, J. Korean Math. Soc., 27(1990), 27 − 30.
  • [12] Kuhnel, W., Conformal transformations between Einstein spaces, Conformal geometry (Bonn, 1985/1986), 105-146, Asepects math., E12, Vieweg, Braunschweig, 1988.
  • [13] Papantoniou, B.J., Contact Riemannian manifolds satisfying R(ξ, X) · R = 0 and ξ ∈ (k, µ)-nullity distribution, Yokohama Math.J., 40(1993), 149 − 161.
  • [14] Pak, J. S., Jeong, J. C. and Kim, W. T., The contact conformal curvature tensor field and the spectrum of the Laplacian, J. Korean. Math. Soc., 28(1991), 267 − 274.
  • [15] Pak, J. S. and Shin, Y. J., A note on contact conformal curvature tensor, Commun. Korean Math. Soc., 13(2)(1998), 337 − 343.
  • [16] Tanno, S., Ricci curvatures of contact Riemannian manifolds, Tôhoku Math. J., 40(1988), 441 − 448 .
  • [17] Yano, K., Concircular geometry I. concircular transformations, Proc. Imp. Acad. Tokyo, 16(1940), 195-200.
  • [18] Yildiz, A. and De, U. C., A classification of (k, µ)-contact metric manifolds, Commun. Korean Math. Soc., 27(2012), 327-339.
There are 18 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

U.c. De

Srimayee Samui This is me

Publication Date April 30, 2017
Submission Date August 20, 2016
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA De, U., & Samui, S. (2017). On a Subclass of (k, µ)-Contact Metric Manifolds. Mathematical Sciences and Applications E-Notes, 5(1), 9-18. https://doi.org/10.36753/mathenot.421477
AMA De U, Samui S. On a Subclass of (k, µ)-Contact Metric Manifolds. Math. Sci. Appl. E-Notes. April 2017;5(1):9-18. doi:10.36753/mathenot.421477
Chicago De, U.c., and Srimayee Samui. “On a Subclass of (k, )-Contact Metric Manifolds”. Mathematical Sciences and Applications E-Notes 5, no. 1 (April 2017): 9-18. https://doi.org/10.36753/mathenot.421477.
EndNote De U, Samui S (April 1, 2017) On a Subclass of (k, µ)-Contact Metric Manifolds. Mathematical Sciences and Applications E-Notes 5 1 9–18.
IEEE U. De and S. Samui, “On a Subclass of (k, µ)-Contact Metric Manifolds”, Math. Sci. Appl. E-Notes, vol. 5, no. 1, pp. 9–18, 2017, doi: 10.36753/mathenot.421477.
ISNAD De, U.c. - Samui, Srimayee. “On a Subclass of (k, )-Contact Metric Manifolds”. Mathematical Sciences and Applications E-Notes 5/1 (April 2017), 9-18. https://doi.org/10.36753/mathenot.421477.
JAMA De U, Samui S. On a Subclass of (k, µ)-Contact Metric Manifolds. Math. Sci. Appl. E-Notes. 2017;5:9–18.
MLA De, U.c. and Srimayee Samui. “On a Subclass of (k, )-Contact Metric Manifolds”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 1, 2017, pp. 9-18, doi:10.36753/mathenot.421477.
Vancouver De U, Samui S. On a Subclass of (k, µ)-Contact Metric Manifolds. Math. Sci. Appl. E-Notes. 2017;5(1):9-18.

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