# Abnormality of trajectory in sub-Riemannian structure

Banach Center Publications (1995)

- Volume: 32, Issue: 1, page 301-317
- ISSN: 0137-6934

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topPelletier, F., and Bouche, L.. "Abnormality of trajectory in sub-Riemannian structure." Banach Center Publications 32.1 (1995): 301-317. <http://eudml.org/doc/262701>.

@article{Pelletier1995,

abstract = {In the sub-Riemannian framework, we give geometric necessary and sufficient conditions for the existence of abnormal extremals of the Maximum Principle. We give relations between abnormality, $C^1$-rigidity and length minimizing. In particular, in the case of three dimensional manifolds we show that, if there exist abnormal extremals, generically, they are locally length minimizing and in the case of four dimensional manifolds we exhibit abnormal extremals which are not $C^1$-rigid and which can be minimizing or non minimizing according to different metrics.},

author = {Pelletier, F., Bouche, L.},

journal = {Banach Center Publications},

keywords = {rigidity; sub-Riemannian manifold; arc minimizing curves; abnormal extremal; Pontryagin maximum principle},

language = {eng},

number = {1},

pages = {301-317},

title = {Abnormality of trajectory in sub-Riemannian structure},

url = {http://eudml.org/doc/262701},

volume = {32},

year = {1995},

}

TY - JOUR

AU - Pelletier, F.

AU - Bouche, L.

TI - Abnormality of trajectory in sub-Riemannian structure

JO - Banach Center Publications

PY - 1995

VL - 32

IS - 1

SP - 301

EP - 317

AB - In the sub-Riemannian framework, we give geometric necessary and sufficient conditions for the existence of abnormal extremals of the Maximum Principle. We give relations between abnormality, $C^1$-rigidity and length minimizing. In particular, in the case of three dimensional manifolds we show that, if there exist abnormal extremals, generically, they are locally length minimizing and in the case of four dimensional manifolds we exhibit abnormal extremals which are not $C^1$-rigid and which can be minimizing or non minimizing according to different metrics.

LA - eng

KW - rigidity; sub-Riemannian manifold; arc minimizing curves; abnormal extremal; Pontryagin maximum principle

UR - http://eudml.org/doc/262701

ER -

## References

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