On ?-Ricci Recurrent Almost Kenmotsu Manifolds with Nullity Distributions

On ?-Ricci Recurrent Almost Kenmotsu Manifolds with Nullity Distributions

The purpose of this paper is to investigate?-Ricci recurrent and?-Ricci symmetric almostKenmotsu manifolds with its characteristic vector field?belonging to some nullity distributions.Also we obtain several corollaries. Finally, we give an example of aKenmotsu manifold such that?belongs to the(k, µ)0-nullity distribution andh06= 0.-dimensional almost.

___

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