Conjugate loci of pseudo-Riemannian 2-step nilpotent Lie groups with nondegenerate center
Parker, Phillip E.
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Jang, C. and P. E. Parker (2005). Conjugate loci of pseudoriemannian 2-step nilpotent Lie groups with nondegenerate center. Annals of Global Analysis and Geometry 28: 1–18.
We determine the complete conjugate locus along all geodesics parallel or perpendicular to the center (Theorem 2.3). When the center is one-dimensional we obtain formulas in all cases (Theorem 2.5), and when a certain operator is also diagonalizable these formulas become completely explicit (Corollary 2.7). These yield some new information about the smoothness of the pseudoriemannian conjugate locus. We also obtain the multiplicities of all conjugate points.
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