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On ϕ-Ricci Recurrent Almost Kenmotsu Manifolds with Nullity Distributions

Year 2016, Volume: 9 Issue: 2, 70 - 79, 30.10.2016
https://doi.org/10.36890/iejg.584599

Abstract

References

  • [1] Blair, D.E., Contact manifold in Riemannian geometry. Lecture Notes on Mathematics. Springer, Berlin, 509, 1976.
  • [2] Blair, D.E., Riemannian geometry on contact and symplectic manifolds. Progr. Math. 203, Birkhäuser, 2010.
  • [3] Blair, D.E., Koufogiorgos, T. and Papantoniou, B.J., Contact metric manifolds satisfying a nullity condition. Israel J. Math. 91 (1995), 189-214.
  • [4] De, U.C., On ϕ-symmetric Kenmotsu manifolds. Int. Electron. J. Geom. 1 (2008), 33-38.
  • [5] De, U.C., Sarkar, A., On ϕ-Ricci symmetric Sasakian manifolds. Proc. of the Jangjeon Math. Soc. 11 (2008), 47-52.
  • [6] De, U.C., Shaikh, A.A. and Biswas, S., On ϕ-recurrent Sasakian manifolds. Novi Sad J. Math. 33 (2003), 43-48.
  • [7] De, U.C., Yildiz, A. and Yaliniz, A.F., On ϕ-recurrent Kenmotsu manifolds. Turkish J. Math. 33 (2009), 17-25.
  • [8] De, U.C., Yildiz, A. and Yaliniz, A.F., Locally ϕ-symmetric normal almost contact metric manifolds of dimension 3. Applied Math. Letters. 22 (2009), 723-727.
  • [9] Dileo, G. and Pastore, A.M., Almost Kenmotsu manifolds and local symmetry. Bull. Belg. Math. Soc. Simon Stevin. 14 (2007), 343-354.
  • [10] Dileo, G. and Pastore, A.M., Almost Kenmotsu manifolds and nullity distributions. J. Geom. 93 (2009), 46-61.
  • [11] Dileo, G. and Pastore, A.M., Almost Kenmotsu manifolds with a condition of ϕ-parallelism. Differential Geom. Appl. 27 (2009), 671-679.
  • [12] Gray, A., Spaces of constancy of curvature operators. Proc. Amer. Math. Soc. 17 (1966), 897-902.
  • [13] Kenmotsu, K., A class of almost contact Riemannian manifolds. Tohoku Math. J. 24 (1972), 93-103.
  • [14] Pastore, A.M. and Saltarelli, V., Generalized nullity distributions on almost Kenmotsu manifolds. Int. Electron. J. Geom. 4 (2011), 168-183.
  • [15] Takahashi, T., Sasakian ϕ-symmetic spaces. Tohoku Math. J. 29 (1977), 91-113.
  • [16] Tanno, S., Some differential equations on Riemannian manifolds. J. Math. Soc. Japan. 30 (1978), 509-531.
  • [17] Wang, Y. and Liu, X., Second order parallel tensors on almost Kenmotsu manifolds satisfying the nullity distributions. Filomat. 28 (2014), 839-847.
  • [18] Wang, Y. and Liu, X., Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions. Ann. Polon. Math. 112 (2014), 37-46.
  • [19] Wang, Y. and Liu, X., On ϕ-recurrent almost Kenmotsu manifolds. Kuwait J. Sci. 42 (2015), 65-77.
  • [20] Wang, Y. and Liu, X., On a type of almost Kenmotsu manifolds with harmonic curvature tensors. Bull. Belg. Math. Soc. Simon Stevin. 22 (2015), 15-24.
  • [21] Wang, Y. and Liu, X., On almost Kenmotsu manifolds satisfying some nullity distributions. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 86 (2016), 347-353.
Year 2016, Volume: 9 Issue: 2, 70 - 79, 30.10.2016
https://doi.org/10.36890/iejg.584599

Abstract

References

  • [1] Blair, D.E., Contact manifold in Riemannian geometry. Lecture Notes on Mathematics. Springer, Berlin, 509, 1976.
  • [2] Blair, D.E., Riemannian geometry on contact and symplectic manifolds. Progr. Math. 203, Birkhäuser, 2010.
  • [3] Blair, D.E., Koufogiorgos, T. and Papantoniou, B.J., Contact metric manifolds satisfying a nullity condition. Israel J. Math. 91 (1995), 189-214.
  • [4] De, U.C., On ϕ-symmetric Kenmotsu manifolds. Int. Electron. J. Geom. 1 (2008), 33-38.
  • [5] De, U.C., Sarkar, A., On ϕ-Ricci symmetric Sasakian manifolds. Proc. of the Jangjeon Math. Soc. 11 (2008), 47-52.
  • [6] De, U.C., Shaikh, A.A. and Biswas, S., On ϕ-recurrent Sasakian manifolds. Novi Sad J. Math. 33 (2003), 43-48.
  • [7] De, U.C., Yildiz, A. and Yaliniz, A.F., On ϕ-recurrent Kenmotsu manifolds. Turkish J. Math. 33 (2009), 17-25.
  • [8] De, U.C., Yildiz, A. and Yaliniz, A.F., Locally ϕ-symmetric normal almost contact metric manifolds of dimension 3. Applied Math. Letters. 22 (2009), 723-727.
  • [9] Dileo, G. and Pastore, A.M., Almost Kenmotsu manifolds and local symmetry. Bull. Belg. Math. Soc. Simon Stevin. 14 (2007), 343-354.
  • [10] Dileo, G. and Pastore, A.M., Almost Kenmotsu manifolds and nullity distributions. J. Geom. 93 (2009), 46-61.
  • [11] Dileo, G. and Pastore, A.M., Almost Kenmotsu manifolds with a condition of ϕ-parallelism. Differential Geom. Appl. 27 (2009), 671-679.
  • [12] Gray, A., Spaces of constancy of curvature operators. Proc. Amer. Math. Soc. 17 (1966), 897-902.
  • [13] Kenmotsu, K., A class of almost contact Riemannian manifolds. Tohoku Math. J. 24 (1972), 93-103.
  • [14] Pastore, A.M. and Saltarelli, V., Generalized nullity distributions on almost Kenmotsu manifolds. Int. Electron. J. Geom. 4 (2011), 168-183.
  • [15] Takahashi, T., Sasakian ϕ-symmetic spaces. Tohoku Math. J. 29 (1977), 91-113.
  • [16] Tanno, S., Some differential equations on Riemannian manifolds. J. Math. Soc. Japan. 30 (1978), 509-531.
  • [17] Wang, Y. and Liu, X., Second order parallel tensors on almost Kenmotsu manifolds satisfying the nullity distributions. Filomat. 28 (2014), 839-847.
  • [18] Wang, Y. and Liu, X., Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions. Ann. Polon. Math. 112 (2014), 37-46.
  • [19] Wang, Y. and Liu, X., On ϕ-recurrent almost Kenmotsu manifolds. Kuwait J. Sci. 42 (2015), 65-77.
  • [20] Wang, Y. and Liu, X., On a type of almost Kenmotsu manifolds with harmonic curvature tensors. Bull. Belg. Math. Soc. Simon Stevin. 22 (2015), 15-24.
  • [21] Wang, Y. and Liu, X., On almost Kenmotsu manifolds satisfying some nullity distributions. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 86 (2016), 347-353.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

U.c. De

Krishanu Mandal

Publication Date October 30, 2016
Published in Issue Year 2016 Volume: 9 Issue: 2

Cite

APA De, U., & Mandal, K. (2016). On ϕ-Ricci Recurrent Almost Kenmotsu Manifolds with Nullity Distributions. International Electronic Journal of Geometry, 9(2), 70-79. https://doi.org/10.36890/iejg.584599
AMA De U, Mandal K. On ϕ-Ricci Recurrent Almost Kenmotsu Manifolds with Nullity Distributions. Int. Electron. J. Geom. October 2016;9(2):70-79. doi:10.36890/iejg.584599
Chicago De, U.c., and Krishanu Mandal. “On ϕ-Ricci Recurrent Almost Kenmotsu Manifolds With Nullity Distributions”. International Electronic Journal of Geometry 9, no. 2 (October 2016): 70-79. https://doi.org/10.36890/iejg.584599.
EndNote De U, Mandal K (October 1, 2016) On ϕ-Ricci Recurrent Almost Kenmotsu Manifolds with Nullity Distributions. International Electronic Journal of Geometry 9 2 70–79.
IEEE U. De and K. Mandal, “On ϕ-Ricci Recurrent Almost Kenmotsu Manifolds with Nullity Distributions”, Int. Electron. J. Geom., vol. 9, no. 2, pp. 70–79, 2016, doi: 10.36890/iejg.584599.
ISNAD De, U.c. - Mandal, Krishanu. “On ϕ-Ricci Recurrent Almost Kenmotsu Manifolds With Nullity Distributions”. International Electronic Journal of Geometry 9/2 (October 2016), 70-79. https://doi.org/10.36890/iejg.584599.
JAMA De U, Mandal K. On ϕ-Ricci Recurrent Almost Kenmotsu Manifolds with Nullity Distributions. Int. Electron. J. Geom. 2016;9:70–79.
MLA De, U.c. and Krishanu Mandal. “On ϕ-Ricci Recurrent Almost Kenmotsu Manifolds With Nullity Distributions”. International Electronic Journal of Geometry, vol. 9, no. 2, 2016, pp. 70-79, doi:10.36890/iejg.584599.
Vancouver De U, Mandal K. On ϕ-Ricci Recurrent Almost Kenmotsu Manifolds with Nullity Distributions. Int. Electron. J. Geom. 2016;9(2):70-9.