Annals of Global Analysis and Geometry

, Volume 28, Issue 1, pp 1–18

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

Article

DOI: 10.1007/s10455-005-5430-8

Cite this article as:
Jang, C. & Parker, P.E. Ann Glob Anal Geom (2005) 28: 1. doi:10.1007/s10455-005-5430-8

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.

Key words

nilpotent Lie groups Riemannian geometry pseudo-Riemannian conjugate locus 

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Mathematics DepartmentWichita, State UniversityWichitaU.S.A.
  2. 2.Department of Mathematics, College of Natural SciencesUniversity of UlsanUlsanRepublic of Korea

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