  We construct some examples of D=3, N=4 GW theory and N=5 superconformal
Chern-Simons matter theory by using the covariantly constant curvature of a
quaternionic-Kahler manifold to construct the symplectic 3-algebra in the
theories. Comparing with the previous theories, the N=4, 5 theories constructed
in this way possess a local Sp(2n) symmetry and a diffeomorphism symmetry
associated with the quaternionic-Kahler manifold. We also construct a
generalized N=8 BLG theory by utilizing the dual curvature operator of a
maximally symmetric space of dimension 4 to construct the Nambu 3-algebra.
Comparing with the previous N=8 BLG theory, the theory has a diffeomorphism
invariance and a local SO(4) invariance associated with the symmetric space.
