# Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity

Andrei A. Agrachev; Andrei V. Sarychev

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 4, page 377-403
- ISSN: 1292-8119

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topAgrachev, Andrei A., and Sarychev, Andrei V.. "Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 377-403. <http://eudml.org/doc/197295>.

@article{Agrachev2010,

abstract = {
We study sub-Riemannian (Carnot-Caratheodory) metrics defined by
noninvolutive distributions on real-analytic Riemannian manifolds.
We establish a connection between regularity properties of these
metrics and the lack of length minimizing abnormal geodesics.
Utilizing the results of the previous study of abnormal length
minimizers accomplished by the authors in [Annales IHP. Analyse
nonlinéaire 13, p. 635-690] we describe in this
paper two classes of the germs of distributions (called
2-generating and medium fat) such that the corresponding
sub-Riemannian metrics are subanalytic. To characterize these
classes of distributions we determine the dimensions of the
manifolds on which generic germs of distributions of given rank
are respectively 2-generating or medium fat.
},

author = {Agrachev, Andrei A., Sarychev, Andrei V.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Sub-Riemannian metrics; subanalitycity; abnormal length minimizers.; abnormal length minimizer; Carnot-Carathéodory metrics; noninvolutive distributions; abnormal geodesics; sub-Riemannian metrics; subanalytic},

language = {eng},

month = {3},

pages = {377-403},

publisher = {EDP Sciences},

title = {Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity},

url = {http://eudml.org/doc/197295},

volume = {4},

year = {2010},

}

TY - JOUR

AU - Agrachev, Andrei A.

AU - Sarychev, Andrei V.

TI - Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 4

SP - 377

EP - 403

AB -
We study sub-Riemannian (Carnot-Caratheodory) metrics defined by
noninvolutive distributions on real-analytic Riemannian manifolds.
We establish a connection between regularity properties of these
metrics and the lack of length minimizing abnormal geodesics.
Utilizing the results of the previous study of abnormal length
minimizers accomplished by the authors in [Annales IHP. Analyse
nonlinéaire 13, p. 635-690] we describe in this
paper two classes of the germs of distributions (called
2-generating and medium fat) such that the corresponding
sub-Riemannian metrics are subanalytic. To characterize these
classes of distributions we determine the dimensions of the
manifolds on which generic germs of distributions of given rank
are respectively 2-generating or medium fat.

LA - eng

KW - Sub-Riemannian metrics; subanalitycity; abnormal length minimizers.; abnormal length minimizer; Carnot-Carathéodory metrics; noninvolutive distributions; abnormal geodesics; sub-Riemannian metrics; subanalytic

UR - http://eudml.org/doc/197295

ER -

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