On Three Dimensional $$C_{12}$$-Manifolds

Legendre curves on 3-dimensional $C_{12}$-Manifolds

“…C 12 -manifolds arose in a natural way from the classification of almost contact metric structures by D. Chinea and C. Gonzalez [8] in 1990. Recently, these manifolds was studied and most of its properties were deduced in [6], especially [4]. As C 12 -manifolds differs from the above almost contact metric manifolds, at least in the normality property, in the present paper, we will show that the results related to Legendre curves in 3-dimentional C 12 -manifolds are fundamentally different from the results in other almost contact metric manifolds.…”

“…for all X vector field on M . Moreover, in [4] the (2n + 1)-dimensional C 12 -manifolds is also characterized by…”

“…In [4], the authors studied the 3-dimensional unit C 12 -manifold i.e. the case where ψ is a unit vector field.…”

Three-dimensional $C_{12}$-manifolds

“…This class is defined by using a certain function α and when this function vanishes the class C 5 ⊕ C 12 reduces to class C 12 . The second paper [3] contains new results on a particular three-dimensional C 12 -manifolds with a class of concrete illustrative examples.…”

Almost contact metric manifolds with certain condition

“…A. Oubiña [7]. Recently, in [3], the authors studied the 3-dimensional C 12 -structure which is integrable non-normal (i.e. N ϕ = 0 and N (1) = 0) and they characterized it by…”