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Year 2019, Volume: 7 Issue: 2, 388 - 394, 15.10.2019

Abstract

References

  • [1] Blair, D. E., Koufogiorgos, T. and Papantoniou, B. J., Contact metric manifolds satisfying a nullity condition, Israel. J. Math. 91(1995), 189-214.
  • [2] Blair, D. E., Contact manifold in Riemannian Geometry. Lecture Notes on Mathematics, Springer, Berlin, 509(1976).
  • [3] Blair, D. E., Riemannian Geometry on contact and symplectic manifolds, Progr. Math., Birkh¨auser, Boston, 203(2010).
  • [4] Dileo, G. and Pastore, A. M., Almost Kenmotsu manifolds and nullity distributions, J. Geom. 93(2009), 46-61.
  • [5] Dileo, G. and Pastore, A. M., Almost Kenmotsu manifolds with a condition of h-parallelsim, Differential Geom. Appl. 27(2009), 671-679.
  • [6] Dileo, G. and Pastore, A. M., Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin, 14(2007), 343-354.
  • [7] De, U. C. and Mandal, K., On a type of almost Kenmotsu manifolds with nullity distributions, Arab J. Math. Sci. 23(2017), 109-123.
  • [8] De, U. C. and Mandal, K., On f-Ricci recurrent almost Kenmotsu manifolds with nullity distributions, Int. Elec. J. Geom. 9(2016), 70-79.
  • [9] Gray, A., Spaces of constancy of curvature operators, Proc. Amer. Math. Soc. 17(1966), 897-902.
  • [10] Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J. 24(1972), 93-103.
  • [11] Mandal, K. and De, U. C., On some classes of 3-dimensional normal almost paracontact metric manifolds, Southeast Asian Bull. Math. 41(2017), 231-238.
  • [12] Pastore, A. M. and Saltarelli, V., Generalized nullity distribution on almost Kenmotsu manifolds, Int. Elec. J. Geom. 4(2011), 168-183.
  • [13] Pastore, A. M. and Saltarelli, V., Almost Kenmotsu manifolds with conformal Reeb foliation, Bull. Belg. Math. Soc. Simon Stevin, 18(2011), 655-666.
  • [14] Tanno, S., Some differential equations on Riemannian manifolds, J. Math. Soc. Japan, 30(1978), 509-531.
  • [15] Wang, Y. and Liu, X., On f-recurrent almost Kenmotsu manifolds, Kuwait J. Sci. 42(2015), 65-77.
  • [16] Wang, Y. and Liu, X., Riemannian semi-symmetric almost Kenmotsu manifolds and nullity distributions, Ann. Polon. Math. 112(2014), 37-46.
  • [17] Zhen, G., Cabrerizo, J.L., Fern ´ andez, L.M. and Fern ´ andez, M., On x -conformally flat contact metric manifolds, Indian J. Pure Appl. Math. 28(1997), 725-734.

A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds

Year 2019, Volume: 7 Issue: 2, 388 - 394, 15.10.2019

Abstract

The object of the present paper is to characterize $\xi$-conformally flat $(k,\mu)$-almost Kenmotsu manifolds and $(k,\mu)'$-almost Kenmotsu manifolds. It is proved that a $(k,\mu)$-almost Kenmotsu manifold is $\xi$-conformally flat if and only if the manifold is an Einstein manifold. Further it is shown that a $(2n+1)$-dimensional $(k,\mu)'$-almost Kenmotsu manifold is $\xi$-conformally flat if and only if it is conformally flat. As a consequence of the main results we obtain several corollaries. Finally, we give an example to verify our result.

References

  • [1] Blair, D. E., Koufogiorgos, T. and Papantoniou, B. J., Contact metric manifolds satisfying a nullity condition, Israel. J. Math. 91(1995), 189-214.
  • [2] Blair, D. E., Contact manifold in Riemannian Geometry. Lecture Notes on Mathematics, Springer, Berlin, 509(1976).
  • [3] Blair, D. E., Riemannian Geometry on contact and symplectic manifolds, Progr. Math., Birkh¨auser, Boston, 203(2010).
  • [4] Dileo, G. and Pastore, A. M., Almost Kenmotsu manifolds and nullity distributions, J. Geom. 93(2009), 46-61.
  • [5] Dileo, G. and Pastore, A. M., Almost Kenmotsu manifolds with a condition of h-parallelsim, Differential Geom. Appl. 27(2009), 671-679.
  • [6] Dileo, G. and Pastore, A. M., Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin, 14(2007), 343-354.
  • [7] De, U. C. and Mandal, K., On a type of almost Kenmotsu manifolds with nullity distributions, Arab J. Math. Sci. 23(2017), 109-123.
  • [8] De, U. C. and Mandal, K., On f-Ricci recurrent almost Kenmotsu manifolds with nullity distributions, Int. Elec. J. Geom. 9(2016), 70-79.
  • [9] Gray, A., Spaces of constancy of curvature operators, Proc. Amer. Math. Soc. 17(1966), 897-902.
  • [10] Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J. 24(1972), 93-103.
  • [11] Mandal, K. and De, U. C., On some classes of 3-dimensional normal almost paracontact metric manifolds, Southeast Asian Bull. Math. 41(2017), 231-238.
  • [12] Pastore, A. M. and Saltarelli, V., Generalized nullity distribution on almost Kenmotsu manifolds, Int. Elec. J. Geom. 4(2011), 168-183.
  • [13] Pastore, A. M. and Saltarelli, V., Almost Kenmotsu manifolds with conformal Reeb foliation, Bull. Belg. Math. Soc. Simon Stevin, 18(2011), 655-666.
  • [14] Tanno, S., Some differential equations on Riemannian manifolds, J. Math. Soc. Japan, 30(1978), 509-531.
  • [15] Wang, Y. and Liu, X., On f-recurrent almost Kenmotsu manifolds, Kuwait J. Sci. 42(2015), 65-77.
  • [16] Wang, Y. and Liu, X., Riemannian semi-symmetric almost Kenmotsu manifolds and nullity distributions, Ann. Polon. Math. 112(2014), 37-46.
  • [17] Zhen, G., Cabrerizo, J.L., Fern ´ andez, L.M. and Fern ´ andez, M., On x -conformally flat contact metric manifolds, Indian J. Pure Appl. Math. 28(1997), 725-734.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Dibakar Dey

Publication Date October 15, 2019
Submission Date April 1, 2019
Acceptance Date July 19, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Dey, D. (2019). A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds. Konuralp Journal of Mathematics, 7(2), 388-394.
AMA Dey D. A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds. Konuralp J. Math. October 2019;7(2):388-394.
Chicago Dey, Dibakar. “A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds”. Konuralp Journal of Mathematics 7, no. 2 (October 2019): 388-94.
EndNote Dey D (October 1, 2019) A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds. Konuralp Journal of Mathematics 7 2 388–394.
IEEE D. Dey, “A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds”, Konuralp J. Math., vol. 7, no. 2, pp. 388–394, 2019.
ISNAD Dey, Dibakar. “A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds”. Konuralp Journal of Mathematics 7/2 (October 2019), 388-394.
JAMA Dey D. A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds. Konuralp J. Math. 2019;7:388–394.
MLA Dey, Dibakar. “A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds”. Konuralp Journal of Mathematics, vol. 7, no. 2, 2019, pp. 388-94.
Vancouver Dey D. A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds. Konuralp J. Math. 2019;7(2):388-94.
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