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Let n be a 2-step nilpotent Lie algebra which has an inner product ⟨ , ⟩ and has an orthogonal decomposition n = z ⊕ v for its center z and the orthogonal complement v of z. Then Each element z of z defines a skew symmetric linear map Jz : v −→ v given by ⟨Jzx, y⟩ = ⟨z, (x, y)⟩ for all x, y ∈ v. In this paper we characterize Jacobi fields and calculate all conjugate points of a simply connected 2-step nilpotent Lie group N with its Lie algebra n satisfying J 2 z = ⟨Sz, z⟩A for all z ∈ z, where S is a positive definite symmetric operator on z and A is a negative definite symmetric operator on v.

CONJUGATE LOCI OF 2-STEP NILPOTENT LIE GROUPS SATISFYING J2z= <Sz, z>A

CONJUGATE LOCI OF 2-STEP NILPOTENT LIE GROUPS SATISFYING J²_z= <Sz, z>A