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Displaying similar documents to “On complexity and motion planning for co-rank one sub-riemannian metrics”

Projective Reeds-Shepp car on with quadratic cost

Ugo Boscain, Francesco Rossi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Fix two points x , x ¯ ∈ S 2 and two directions (without orientation) η , η ¯ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost J [ γ ] = ∫ 0 T γ ( t ) ( γ ˙ ( t ) , γ ˙ ( t ) ) + K γ ( t ) 2 γ ( t ) ( γ ˙ ( t ) , γ ˙ ( t ) ) d t along all smooth curves starting from x with direction η and ending in x ¯ with direction η ¯ . Here g is the standard Riemannian metric on S 2...

On natural metrics on tangent bundles of Riemannian manifolds

Mohamed Tahar Kadaoui Abbassi, Maâti Sarih (2005)

Archivum Mathematicum

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There is a class of metrics on the tangent bundle T M of a Riemannian manifold ( M , g ) (oriented , or non-oriented, respectively), which are ’naturally constructed’ from the base metric g [Kow-Sek1]. We call them “ g -natural metrics" on T M . To our knowledge, the geometric properties of these general metrics have not been studied yet. In this paper, generalizing a process of Musso-Tricerri (cf. [Mus-Tri]) of finding Riemannian metrics on T M from some quadratic forms on O M × ℝ m to find metrics (not necessary...