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

Title & Authors
CONJUGATE LOCI OF 2-STEP NILPOTENT LIE GROUPS SATISFYING J2z = <Sz, z>A
Jang, Chang-Rim; Lee, Tae-Hoon; Park, Keun;

Abstract
Let n be a 2-step nilpotent Lie algebra which has an inner product <, > and has an orthogonal decomposition $\small{n\;=z\;{\oplus}v}$ for its center z and the orthogonal complement v of z. Then Each element z of z defines a skew symmetric linear map $\small{J_z\;:\;v\;{\longrightarrow}\;v}$ given by <$\small{J_zx}$, y> = for all x, $\small{y\;{\in}\;v}$. 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 $\small{J^2_z}$ = A for all $\small{z\;{\in}\;z}$, where S is a positive definite symmetric operator on z and A is a negative definite symmetric operator on v.
Keywords
2-step nilpotent Lie groups;Jacobi fields;conjugate points;
Language
English
Cited by
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