You will find as you look back upon your life that the moments when you have truly lived are the moments when you have done things in the spirit of love.
by Henry Drummond

SubRiemannian

In 2007-2008 I’ll give an introductory Master course (36h of lectures) on diferential geometry and subRiemannian geometry. This page is used for my preparation of the course.

Topics that I want to cover (on sub-Riemannian geometry)

* Non-integrable distributions and their normal forms ?

* Sub-Riemannian metric and sub-Riemannian distance

* Chow theorem: bracket generating condition –> any two points can be connected by a horizontal path

*Existence of geodesics ?

* Nonholonomic derivatives, nonholonomic degree of functions and vector fields

* Growth vector, privileged coordinates

* Ball-Box theorem

* Nilpotent approximation (homogenization), tangent metric spaces

* Hausdorff dimension and Hausdorff measure

* Singular horizontal curves, abnormal geodesics

* Applications and related topics:� control theory ?� holomorphic functions ? Kaluza-Klein theory ? isoperimetric problems ? geometric phases in mechanics ? hyperbolic groups ?

Recommended References :

* F. Jean, Sub-Riemannian Geometry, notes of the lectures given in Trieste, 2003. [Very good introductory notes, though unfortunately they are incomplete]

* R. Montgomery, A tour of Riemannian geometry, 2001. [A nice book about subRiemannian geometry and some of its applications. Warning: the proof of the ball-box theorem in this book is not correct]

* …

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