Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CONJUGATE LOCI OF 2-STEP NILPOTENT LIE GROUPS SATISFYING J2z = <Sz, z>A

  • Jang, Chang-Rim (DEPARTMENT OF MATHEMATICS COLLEGE OF NATURAL SCIENCES UNIVERSITY OF ULSAN) ;
  • Lee, Tae-Hoon (DEPARTMENT OF MATHEMATICS COLLEGE OF NATURAL SCIENCES UNIVERSITY OF ULSAN) ;
  • Park, Keun (DEPARTMENT OF MATHEMATICS COLLEGE OF NATURAL SCIENCES UNIVERSITY OF ULSAN)
  • Published : 2008.11.01
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Abstract

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

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References

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