Zobrazeno 1 - 10
of 14
pro vyhledávání: '"Mauricio Godoy Molina"'
Autor:
Mauricio Godoy Molina, Irina Markina
Publikováno v:
Lecture Notes in Electrical Engineering ISBN: 9783030586522
We study the interplay between geodesics on two non-holonomic systems that are related by the action of a Lie group on them. After some geometric preliminaries, we use the Hamiltonian formalism to write the parametric form of geodesics. We present se
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e7317166c1a4c1ce6fe9cecea26eddf9
https://doi.org/10.1007/978-3-030-58653-9_8
https://doi.org/10.1007/978-3-030-58653-9_8
Autor:
Mauricio Godoy Molina
Publikováno v:
Analysis and Mathematical Physics. 8:485-491
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::40a064cf896474d8927721ef459e8021
https://doi.org/10.1007/s13324-018-0260-6
https://doi.org/10.1007/s13324-018-0260-6
Autor:
Mauricio Godoy Molina, Erlend Grong
Publikováno v:
The Journal of Geometric Analysis. 27:1260-1273
In the present paper we show that the geodesic flows of a sub-Riemannian metric and that of a Riemannian extension commute if and only if the extended metric is parallel with respect to a certain connection. This helps us to describe the geodesic flo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df8afed08e75c1241d80e64e8d67faa4
https://doi.org/10.1007/s12220-016-9717-8
https://doi.org/10.1007/s12220-016-9717-8
Publikováno v:
Mathematische Nachrichten. 289:4-12
In the present paper we prove that the sub-Riemannian cut locus at the origin of a wide class of nilpotent groups of step two, called H-type groups, corresponds to the center of the group. We obtain this result by completely describing the sub-Rieman
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4e2a1a285d7bafb91b04df7a8d4301bf
https://doi.org/10.1002/mana.201400368
https://doi.org/10.1002/mana.201400368
Autor:
Mauricio Godoy Molina, Erlend Grong
Publikováno v:
Communications on Pure & Applied Analysis. 13:435-452
We give a complete answer to the question of when two curves in two different Riemannian manifolds can be seen as trajectories of rolling one manifold on the other without twisting or slipping. We show that, up to technical hypotheses, a rolling alon
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0437c2a7f4bf2bd78fab17de7ae92b42
https://doi.org/10.3934/cpaa.2014.13.435
https://doi.org/10.3934/cpaa.2014.13.435
In the present paper we study the rigidity of 2-step Carnot groups, or equivalently, of graded 2-step nilpotent Lie algebras. We prove the alternative that depending on bi-dimensions of the algebra, the Lie algebra structure makes it either always of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2f3557560e6e5031c5de9b605a979696
https://hdl.handle.net/10037/14214
https://hdl.handle.net/10037/14214
Publikováno v:
Analysis, Modelling, Optimization, and Numerical Techniques ISBN: 9783319125824
In this chapter, we study sub-Riemannian geodesics in the octonionic H-type group \(G_7^1\), which is a nilpotent group of step 2 and, as a manifold, diffeomorphic to \({\mathbb R}^{15}\).
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9342c35a1b950a95d74f11207ad0e97f
https://doi.org/10.1007/978-3-319-12583-1_8
https://doi.org/10.1007/978-3-319-12583-1_8
Publikováno v:
The Journal of Geometric Analysis
The Journal of Geometric Analysis, Springer, 2016, 26 (4), pp.2542-2562. ⟨10.1007/s12220-015-9638-y⟩
The Journal of Geometric Analysis, Springer, 2016, 26 (4), pp.2542-2562. ⟨10.1007/s12220-015-9638-y⟩
We study the control system of a Riemannian manifold $M$ of dimension $n$ rolling on the sphere $S^n$. The controllability of this system is described in terms of the holonomy of a vector bundle connection which, we prove, is isomorphic to the Rieman
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2f5c59b82352b337e45dfde7a48dab0a
http://arxiv.org/abs/1412.7218
http://arxiv.org/abs/1412.7218
Publikováno v:
Mathematische Zeitschrift
Mathematische Zeitschrift, Springer, 2015, 281 (4), pp.783-805. ⟨10.1007/s00209-015-1508-6⟩
Mathematische Zeitschrift, Springer, 2015, 281 (4), pp.783-805. ⟨10.1007/s00209-015-1508-6⟩
In the present paper, we study the infinitesimal symmetries of the model of two Riemannian manifolds $(M,g)$ and $(\hat M,\hat g)$ rolling without twisting or slipping. We show that, under certain genericity hypotheses, the natural bundle projection
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e5043826399fdd3643d59288f7e12032
http://arxiv.org/abs/1301.2579
http://arxiv.org/abs/1301.2579
Publikováno v:
Meeting on Geometric Control Theory and Sub-Riemannian Geometry
Meeting on Geometric Control Theory and Sub-Riemannian Geometry, May 2012, Cortona, Italy. ⟨10.1007/978-3-319-02132-4_7⟩
Geometric Control Theory and Sub-Riemannian Geometry ISBN: 9783319021317
Meeting on Geometric Control Theory and Sub-Riemannian Geometry, May 2012, Cortona, Italy. ⟨10.1007/978-3-319-02132-4_7⟩
Geometric Control Theory and Sub-Riemannian Geometry ISBN: 9783319021317
In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::48a8f8f68f8bba096cf210442b8ca28c
https://hal.archives-ouvertes.fr/hal-02320829
https://hal.archives-ouvertes.fr/hal-02320829