Abstract

We study the geometry of a filiform nilpotent Lie group endowed with a leftinvariant metric. We describe the connection and curvatures, and we investigate necessary and sufficient conditions for subgroups to be totally geodesic submanifolds. We also classify the one-parameter subgroups which are geodesics. Department of Mathematics, Wellesley College, 106 Central St., Wellesley, MA 02481-8203 mkerr@wellesley.edu Department of Mathematics, Idaho State University, Pocatello, ID 83209-8085 payntrac@isu.edu, tpayne@member.ams.org

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