Journal of the
Korean Mathematical Society JKMS

Let $\bullet$ be a 2-step nilpotent Lie algebra which has an inner product $\langle ~, ~\rangle$ and has an orthogonal decomposition $\bullet=\bullet\oplus\bullet$ for its center $\bullet$ and the orthogonal complement $\bullet$ of $\bullet$. Then Each element $z$ of $\bullet$ defines a skew symmetric linear map $J_z:\bullet\longrightarrow \bullet$ given by $\langle J_z x,y\rangle =\langle z,[x,y]\rangle$ for all $x,y\in \bullet$. 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 $\bullet$ satisfying $J_z^2=\langle Sz,z\rangle A$ for all $z\in \bullet$, where $S$ is a positive definite symmetric operator on $\bullet$ and $A$ is a negative definite symmetric operator on $\bullet$.

Keywords: 2-step nilpotent Lie groups, Jacobi fields, conjugate points

MSC numbers: 53C30, 22E25