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Conjugate loci of pseudoriemannian 2-step nilpotent Lie groups with nondegenerate center

Changrim Jang·Phillip E. Parker
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Abstract

We determine the complete conjugate locus along all geodesics parallel or perpendicular to the center (Theorem 2.3). When the center is 1-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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BibTeXRIS

Changrim Jang, Phillip E. Parker. 2005-09-14. Conjugate loci of pseudoriemannian 2-step nilpotent Lie groups with nondegenerate center. https://arxiv.org/abs/math/0302029

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