We consider a 5D extension of the DFSZ axion model that addresses both quality and fermion mass hierarchy problems, predicts flavour-dependent, off-diagonal axion-fermion couplings. The is part complex scalar field charged under U(1)$_{PQ}$ symmetry spontaneously broken in bulk, insensitive to explicit PQ breaking on UV boundary. Bulk Standard Model fermions interact with two Higgs doublets can...

In this paper, we study warped product CR-submanifolds of LP-cosymplectic manifolds. We have shown that the warped product of the type M = NT × fN⊥ does not exist, where NT and N⊥ are invariant and anti-invariant submanifolds of an LP-cosymplectic manifold M̄ , respectively. Also, we have obtained a characterization result for a CR-submanifold to be locally a CRwarped product.

Recently, the present authors considered doubly warped product CR-submanifolds in a locally conformal Kaehler manifold and got some inequalities about the length of the second fundamental form ([14]). In this report, we obtain an inequality of the mean curvature of a doubly warped product CR-submanifold in a locally conformal Kaehler space form. Then, we consider the equality case of this inequ...