Warped Product Skew Semi-Invariant Submanifolds of Nearly Cosymplectic Manifolds

Warped product pointwise hemi-slant submanifolds of a Para-Kaehler manifold

“…Conversely we assume that N is a pointwise hemi-slant submanifold of Ñ such that (21) holds. Taking the inner product of (21) with Y 2 , we can say from Theorem 3.12 that the integral manifold N 1ϕ of D ϕ is totally geodesic foliation in N. Thus, by Corollary 3.9 the distribution D ⊥ is integrable if and only if…”

“…Let us consider that N is a pointwise hemi-slant warped product submanifold of a para-Kaehler manifold Ñ. Then, Lemma 4.5, we have (21). We know that h is a function on N 2 , therefore setting τ = ln h implies that Y 3 (τ) = 0.…”