On the quasi-conformal curvature tensor of an almost Kenmotsu manifold with nullity distributions

Dibakar Dey, Pradip Majhi

DOI Number
https://doi.org/10.22190/FUMI1802255D
First page
255
Last page
268

Abstract


The object of the present paper is to characterize quasi-conformally flat and $\xi$-quasi-conformally flat almost Kenmotsu manifolds with  $(k,\mu)$-nullity and $(k,\mu)'$-nullity distributions respectively. Also we characterize almost Kenmotsu manifolds with vanishing extended quasi-conformal curvature tensor and extended $\xi$-quasi-conformally flat almost Kenmotsu manifolds such that the characteristic vector field $\xi$ belongs to the $(k,\mu)$-nullity distribution.

Keywords

Almost Kenmotsu manifold, Einstein manifold, Weyl conformal curvature tensor, Quasi-conformal curvature tensor, Extended quasi-conformal curvature tensor.

Keywords


Almost Kenmotsu manifold, Einstein manifold, Weyl conformal curvature tensor, Quasi-conformal curvature tensor, Extended quasi-conformal curvature tensor

Full Text:

PDF

References


D. E. Blair, T. Koufogiorgos and B. J. Papantoniou: Contact metric manifolds satisfying a nulitty condition, Israel. J. Math. 91(1995), 189–214.

D. E. Blair: Contact manifold in Reimannian geometry, Lecture notes in Mathematics, Springer, Berlin, 509(1976).

D. E. Blair: Reimannian geometry of contact and symplectic manifolds, Birkh¨auser, Boston, 2002.

B. Y. Chen and K. Yano: Hypersurfaces of a conformally flat space, Tensor (N.S) 26(1972), 318–322.

U. C. De and K. Mandal: On a type of almost Kenmotsu manifolds with nullity distributions, Arab J. Math. Sci. 23(2017), 109–123.

U. C. De and K. Mandal: On -Ricci recurrent almost Kenmotsu manifolds with nullity distributions, Int. Electron. J. Geom. 9(2016), 70–79.

G. Dileo and A. M. Pastore: Almost Kenmotsu manifolds and nullity distributions, J. Geom. 93(2009), 46–61.

G. Dileo and A. M. Pastore: Almost Kenmotsu manifolds with a condition of -parallelsim, Differential Geom. Appl. 27(2009), 671–679.

G. Dileo and A. M. Pastore: Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin 14(2007), 343–354.

A. Gray: Spaces of constancy of curvature operators, Proc. Amer. Math. Soc. 17(1966), 897–902.

K. Kenmotsu: A class of almost contact Riemannian manifolds, Tohoku Math. J., 24(1972), 93–103.

K. Mandal and U. C. De: On some classes of 3-dimensional normal almost paracontact metric manifolds, Southeast Asian Bull. Math. 41(2017), 231–238.

A. M. Pastore and V. Saltarelli: Generalized nullity distribution on almost Kenmotsu manifolds, J. Geom. 4(2011), 168–183.

A. M. Pastore and V. Saltarelli: Almost Kenmotsu manifolds with conformal Reeb foliation, Bull. Belg. Math. Soc. Simon Stevin 21(2012), 343–354.

S. Tanno: Some differential equations on Riemannian manifolds, J. Math. Soc. Japan, 30(1978), 509–531.

Y. Wang and X. Liu: on -recurrent almost Kenmotsu manifolds, Kuwait J. Sci. 42(2015), 65–77.

Y. Wang and X. Liu: Second order parrallel tensors on almost Kenmotsu manifolds satisfying the nullity distributions, Filomat 28(2014), 839–847.

Y. Wang and X. Liu: Riemannian semi-symmetric almost Kenmotsu manifolds and nullity distributions, Ann. Polon. Math. 112(2014), 37–46.

Y. Wang: Conformally flat almost Kenmotsu 3-manifolds, Med. J. Math. 14(2017):186.

Y. Wang: Three dimensional almost Kenmotsu manifolds with -parallel Ricci tensors, J. Korean Math. Soc. 54(2017), 793–805.

K. Yano and S. Sawaki: Riemannian manifolds admitting a conformal transformation group, J. Differential Geom. 2(1968), 161–184.

G. Zhen, J. L. Cabrerizo, L. M. FernA´ndez and M. FernA´ndez: On -conformally




DOI: https://doi.org/10.22190/FUMI1802255D

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)