Some Important Properties of Almost Kenmotsu $\left( \kappa,\mu,\nu\right) -$Space on the Concircular Curvature Tensor

In this article, pseudoparallel submanifolds for almost Kenmotsu $\left( \kappa,\mu,\nu\right) -$space are investigated. The almost Kenmotsu $\left( \kappa,\mu,\nu\right) -$space is considered on the concircular curvature tensor. Submanifolds of these manifolds with properties such as concircular pseudoparallel, concircular $2-$pseudoparallel, concircular Ricci generalized pseudoparallel, and concircular $2-$Ricci generalized pseudoparallel has been characterized. Necessary and sufficient conditions are given for the invariant submanifolds of almost Kenmotsu $\left( \kappa,\mu,\nu\right) -$space to be total geodesic according to the behavior of the $\kappa,\mu,\nu$ functions.

Keywords:

Lorentzian manifold Para-Kenmotsu manifold, Pseudoparallel submanifold,

PDF

___

[1] E. Boeckx, A full classification of contact metric (k;m)?spaces, Illinois J. Math., 44(1) (2000), 212–219.
[2] D. E. Blair, T. Koufogiorgos, B. J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91 (1995), 189–214.
[3] T. Koufogiorgos, M. Markellos, V. J. Papantoniou, The harmonicity of the Reeb vector fields on contact 3?manifolds, Pasific J. Math., 234(2) (2008), 325-344.
[4] A. Carriazo, V. Martin-Molina, Almost cosymplectic and almost Kenmotsu (k;m;n)?Spaces, Mediterr. J. Math., 10 (2013), 1551-1571.
[5] P. Dacko, Z. Olszak, On almost cosymplectic (k;m;n)?spaces, Banach Center Publ., 69(1) (2005), 211-220.
[6] M. Atçeken, Certain results on invariant submanifolds of an almost Kenmotsu (k;m;n)?space, Arab. J. Math., 10 (2021), 543-554.
[7] A. Bejancu, N. Papaghuic, Semi-invariant submanifolds of a Sasakian manifold, Annal Alexandru Ioan Cuza Univ. Ias¸i Math., 27 (1981), 163-170.
[8] M. Atçeken, P. Uygun, Characterizations for totally geodesic submanifolds of (k;m)-paracontact metric manifolds, Korean J. Math., 28(3) (2021), 555-571.
[9] A. De, A note on the paper on invariant submanifolds of LP-Sasakian manifolds, Extracta Math., 28(1) (2013), 33-36.
[10] M. Atçeken, T. Mert, Characterizations for totally geodesic submanifolds of a K-paracontact manifold, AIMS Math., 6(7) (2021),7320-7332.
[11] D. Chinea, P.S. Prestelo, Invariant submanifolds of a trans-Sasakian manifold, Publ. Math. Debrecen, 38(1-2) (1991), 103-109.
[12] M. Atçeken, Some results on invariant submanifolds of Lorentzian para-Kenmotsu manifolds, Korean J. Math., 30(1) (2022), 175-185.
[13] S.K. Hui, V.N. Mishra, T. Pal, Vandana, Some classes of invariant submanifolds of (LCS)n?Manifolds, Italian J.P. Appl. Math., 39 (2018), 359-372.
[14] V. Venkatesha, S. Basavarajappa, Invariant submanifolds of LP-Saakian manifolds, Khayyam J. Math., 6(1) (2020), 16-26.
[15] S. Sular, C. Özgür, C. Murathan, Pseudoparallel anti-invariant submanifolds of Kenmotsu manifolds, Hacet. J. Math. Stat., 39(4) (2010), 535-543.
[16] P. Uygun, S. Dirik, M. Atceken, T. Mert, Some Characterizations Invariant Submanifolds of A (k;m)?Para Contact Space, J. Eng. R. App. Sci., 11(1) (2022), 1967-1972.
[17] M. Atçeken, G. Yüca, Some results on invariant submanifolds of an almost Kenmotsu (k;m;n)?space, Honam Math. J., 43(4) (2021), 655-665.
[18] R. Prasad, Pankaj, On (k;m)?Manifolds with Quasi-conformal Curvature Tensor, Int. J. Contemp. Math. Sciences, 34(5) 2010, 1663- 1676.