CONJUGATE LOCI OF 2-STEP NILPOTENT LIE GROUPS SATISFYING J²z = <Sz, z>A
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Let ㆍ be a 2-step nilpotent Lie algebra which has an inner product < , > and has an orthogonal decomposition ㆍ = ㆍ ㆍ for its center z and the orthogonal complement ㆍ of ㆍ. Then Each element z of ㆍ defines a skew symmetric linear map Jz : ㆍ → ㆍ given by <Jzx, y> = <z, [x, y]> for all x, y ∈ ㆍ. 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 J²z = <Sz, z>A for all z ∈ ㆍ, where S is a positive definite symmetric operator on ㆍ and A is a negative definite symmetric operator on ㆍ.
Abstract
Let ㆍ be a 2-step nilpotent Lie algebra which has an inner product < , > and has an orthogonal decomposition ㆍ = ㆍ ㆍ for its center z and the orthogonal complement ㆍ of ㆍ. Then Each element z of ㆍ defines a skew symmetric linear map Jz : ㆍ → ㆍ given by <Jzx, y> = <z, [x, y]> for all x, y ∈ ㆍ. 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 J²z = <Sz, z>A for all z ∈ ㆍ, where S is a positive definite symmetric operator on ㆍ and A is a negative definite symmetric operator on ㆍ.
참고문헌 (14)
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