, Volume 28, Issue 1, pp 1-18

Conjugate Loci of Pseudo-Riemannian 2-Step Nilpotent Lie Groups with Nondegenerate Center

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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 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.

Mathematics Subject Classifications (2000): primary 53C50; secondary 22E25, 53B30, 53C30.