A tour of subriemannian geometries, their geodesics, and applications / Richard Montgomery.

Author/creator Montgomery, Richard, 1956-
Format Book
Publication InfoProvidence, R.I. : American Mathematical Society, ©2002.
Descriptionxix, 259 pages : illustrations ; 27 cm.
Supplemental ContentTable of contents
Subjects
Geometry, Riemannian.
Geodesics (Mathematics)

SeriesMathematical surveys and monographs, 0076-5376 ; v. 91
Mathematical surveys and monographs no. 91. ^A638333
Contents Geodesics in Subriemannian Manifolds -- Dido Meets Heisenberg -- Dido's problem -- A vector potential -- Heisenberg geometry -- The definition of a subriemannian geometry -- Geodesic equations -- Chow's theorem and geodesic existence -- Geodesic equations on the Heisenberg group -- Why call it the Heisenberg group? -- Proof of the theorem on normal geodesics -- Chow's Theorem: Getting from A to B -- Bracket-generating distributions -- A heuristic proof of Chow's theorem -- The growth vector and canonical flag -- Chow and the ball-box theorem -- Proof of the theorem on topologies -- Privileged coordinates -- Proof of the remaining ball-box inclusion -- Hausdorff measure -- A Remarkable Horizontal Curve -- A rigid curve -- Martinet's genericity result -- The minimality theorem -- The minimality proof of Liu and Sussmann -- Failure of geodesic equations -- Singular curves in higher dimensions -- There are no H[superscript 1]-rigid curves -- Towards a conceptual proof? -- Curvature and Nilpotentization -- The curvature of a distribution -- Dual curvature -- The derived ideal and the big growth vector -- The sheaf of Lie algebras -- Nilpotentization and Carnot groups -- Non-regular nilpotentizations -- Singular Curves and Geodesics -- The space of horizontal paths -- A microlocal characterization -- Singularity and regularity -- Rank-two distributions -- Distributions determined by their curves -- Fat distributions -- A Zoo of Distributions -- Stability and function counting -- The stable types -- Prolongation.
Bibliography noteIncludes bibliographical references (p. 247-255) and index.
LCCN 2001053538
ISBN0821813919 (alk. paper)
ISBN9780821813911 (alk. paper)
ISBN0821841653
ISBN9780821841655

Availability

Library Location Call Number Status Item Actions
Joyner General Stacks QA649 .M73 2002 ✔ Available Place Hold