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

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...

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Bibliographic Details
Published in:arXiv.org 2005-09
Main Authors: Jang, Changrim, Parker, Phillip E
Format: Article
Language:English
Subjects:
Conjugate points
Conjugates
Geodesy
Lie groups
Loci
Smoothness
Theorems
Online Access:Get full text
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Summary: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.
ISSN:2331-8422