Memoirs of the American Mathematical Society 1996; 104 pp; softcover Volume: 118 ISBN10: 0821804049 ISBN13: 9780821804049 List Price: US$44 Individual Members: US$26.40 Institutional Members: US$35.20 Order Code: MEMO/118/564
 This work studies lengthminimizing arcs in subRiemannian manifolds \((M, E, G)\) where the metric \(G\) is defined on a ranktwo bracketgenerating distribution \(E\). The authors define a large class of abnormal extremalsthe "regular" abnormal extremalsand present an analytic technique for proving their local optimality. If \(E\) satisfies a mild additional restrictionvalid in particular for all regular twodimensional distributions and for generic twodimensional distributionsthen regular abnormal extremals are "typical," in a sense made precise in the text. So the optimality result implies that the abnormal minimizers are ubiquitous rather than exceptional. Readership Graduate students, mathematicians, physicists, engineers interested in geometry, optimal control theory, or the calculus of variations. Table of Contents  Introduction
 Three examples
 Notational conventions and definitions
 Abnormal extremals
 SubRiemannian manifolds, length minimizers and extremals
 Regular abnormal extremals for ranktwo distributions
 Local optimality of regular abnormal extremals
 Strict abnormality
 Some special cases
 Appendix A: The GaveauBrockett problem
 Appendix B: Proof of Theorem 1
 Appendix C: Local optimality of normal extremals
 Appendix D: Rigid subRiemannian arcs and local optimality
 Appendix E: A nonoptimality proof
 References
