Ximin Liu, Quanxiang Pan


In this paper, we study 3-dimensional  almost $\alpha$-para-Kenmotsu manifolds satisfying special types of nullity conditions depending on smooth functions $\tilde{\kappa},\tilde{\mu}$ and $\tilde{\nu}$=constant, also we present a local description of the structure of a 3-dimensional almost $\alpha$-para-Kenmotsu $(\tilde{\kappa},\tilde{\mu},\tilde{\nu}=const.)$-manifold $(M,\tilde{\varphi},\xi,\eta,\tilde{g})$ with $\tilde{\kappa}+\alpha^{2}\neq0$ such that $d\tilde{\kappa}\wedge\eta=0$.


Almost paracontact metric manifold; almost $\alpha$-para-Kenmotsu manifold; nullity distribution.

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B. C. Montano and I. K. Erken: Nullity conditions in paracontact geometry. Diff. Geom. Appl. 30 (2012), 665-693.

B. C. Montano and L. D. Terlizzi: Geometric structures associated to a contact metric (, μ)−space. Pacific J. Math. 246 (2010) 257-292.

D. E. Blair: Two remarks on contact metric structures. Tˆohoku Math. J. 29 (1977), 319-324.

D. E. Blair, T. Koufogiorgos and B. J. Papantoniou: Contact metric manifolds satisfying a nullity condition. Israel J. Math. 91 (1995), no. 1-3, 189C214.

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

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

G. Dileo: On the geometry of almost contact metric manifolds of Kenmotsu type. Differential Geom. Appl. 29(2011) 558-564.

H. Öztürk, N. Aktan rm and C. Murathan: Almost -cosymplectic

(, μ, )−spaces. arXiv:1007.0527v1[math.DG]

I. K. Erken, P. Dacko and C. Murathan: Almost a-paracosymplectic manifolds. J. Geom. Phys. 88 (2015), 30-51.

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

T. Koufogiorgos and C. Tsichlias: On the existence of a new class of contact metric manifolds. Canadian Math. Bull. 43(2000), 440-447.

P. Dacko and Z. Olszak: On almost cosymplectic (, μ, )-spaces. Banach Center Publ., 69 2005, 211-220.

P. Dacko: On almost para-cosymplectic manifolds. Tsukuba J. Math. 28 (2004), 193-213.

S. Kaneyuki rm and F. Williams: Almost paracontact and parahodge structures on manifolds. Nagoya Math. J. 99(1985), 173-187.

S. Zamkovoy: Canonical connections on paracontact manifolds. Ann.Glob. Anal. Geom. 36(2009), 37-60.

V. Saltarelli: Three-dimensional almost Kenmotsu manifolds satisfying certain nullity conditions . Bull. Malays. Math. Sci. Soc. 38(2015), 437-459.


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