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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.
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참고문헌 (14)
참고문헌 신청
A. Kaplan / 1981 / Riemannian nilmanifolds attached to Clifford modules / Geometriae Dedicata 11 (2) : 127 ~ 136
A. Kaplan / 1983 / On the geometry of groups of Heisenberg type / Bulletin of the London Mathematical Society 15 (1) : 35 ~ 42
C. Jang / 2000 / Conjugate points on 2-step nilpotent groups / Geometriae Dedicata 79 (1) : 65 ~ 80
C. Jang / 2003 / Conjugate points on the quaternionic Heisenberg group / Journal of the Korean Mathematical Society 40 (1) : 61 ~ 72
C. Jang / 2005 / Conjugate loci of pseudo-Riemannian 2-step nilpotent Lie groups with nondegenerate center / Annals of Global Analysis and Geometry 28 (1) : 1 ~ 18
A. Kaplan / 1983 / On the geometry of groups of Heisenberg type / Bulletin of the London Mathematical Society 15 (1) : 35 ~ 42
C. Jang / 2000 / Conjugate points on 2-step nilpotent groups / Geometriae Dedicata 79 (1) : 65 ~ 80
C. Jang / 2003 / Conjugate points on the quaternionic Heisenberg group / Journal of the Korean Mathematical Society 40 (1) : 61 ~ 72
C. Jang / 2005 / Conjugate loci of pseudo-Riemannian 2-step nilpotent Lie groups with nondegenerate center / Annals of Global Analysis and Geometry 28 (1) : 1 ~ 18
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