Calabi Product Lagrangian Immersions in Complex Projective Space and Complex Hyperbolic Space

Starting from two Lagrangian immersions and a Legendre curve (gamma) over tilde (t) in S-3 (1) (or in H-1(3) (-1)), it is possible to construct a new Lagrangian immersion in CPn (4) (or in CHn (-4)), which is called a warped product Largrangian immersion. When (gamma) over tilde (t) = (r(1)e(2/)(1)(i(r)(r)at()) , r(2)e(i(-)r(1)/r(2)at) (or (gamma) over tilde (t) = (gamma) over tilde (t) = (r(1)e(2/)(1)(i(r)(r)at()) , r(2)e(i(-)r(1)/r(2)at) (or (gamma) over tilde (t), we call the new Largis a Calabi product Lagrangian immersion. When the Calabi product is minimal, or is Hamiltonian minimal, or has parallel second fundamental form, we give some further characterizations.