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

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

2003-02-03

arxiv.org/abs/math/0302029v4

Ann. Global Anal. Geom. 28 (2005) 1--18

Mathematics

Differential Geometry

20 pages + title page; v.2: some proofs simplified; v.3: multiplicities for all conjugate points, some history added; v.4: fin

Scientific paper

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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