Slant Submanifolds of Almost Contact Metric 3-Structure Manifolds

Point-wise slant submanifolds in almost contact geometry

“…where [12]. On these submanifolds for all i = 1, 2, 3, at any point p ∈ M the angle between ϕ i X and T p M is constant for each X ∈ T p M linearly independent of ξ i .…”

“…The author and Malek introduced 3-slant submanifolds of an almost contact metric 3-structure manifold (M , ξ i , η i , ϕ i , g) i∈{1,2,3} [12]. On these submanifolds for all i = 1, 2, 3, at any point p ∈ M the angle between ϕ i X and T p M is constant for each X ∈ T p M linearly independent of ξ i .…”

“…and it follows (12). Conversely, we suppose that α and β are the angles ϕ i X, T i X and ϕ i X, T j X , respectively, in the point p ∈ M .…”

“…In [11], Lotta studied slant submanifolds of contact manifolds that were the generalization of invariant and anti-invariant submanifolds. Since then, many authors have obtained important and interesting results about slant submanifolds of complex [13,14,16,17] and almost contact [1,3,8,12] manifolds.…”

Semi-slant and bi-slant submanifolds of almost contact metric 3-structure manifolds

“…By defining 9 , ∂x 10 , ∂x 11 , in Examples 2 and 3 respectively, M is 3-bi-slant but not 3-slant. A sufficient condition for a 3-bi-slant submanifold with slant angles θ 1 = θ 2 to be a 3-slant submanifold is the following…”