2003/02/28 by Changrim Jang, Phillip E. Parker
Mathematics · #math.DG #msc:53C50 #msc:22E25 #msc:53B30 #msc:53C30
published as Ann. Global Anal. Geom. 28 (2005) 1--18 · 20 pages + title page; v.2: some proofs simplified; v.3: multiplicities for all conjugate points, some history added; v.4: final published version, only minor clarifications from v.3
arxiv created 2005/09/14 · arxiv updated 2009/11/30
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.