no. 4
On contact sub-pseudo-Riemannian isometries
Grochowski, Marek1 ; Kryński, Wojciech2
1 Faculty of Mathematics and Natural Sciences, Cardinal Wyszyński University, 01-938 Warszawa, Poland.
2 Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warszawa, Poland.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1751-1765

We study isometries in contact sub-pseudo-Riemannian geometry. In particular we give an upper bound on the dimension of the isometry group of a general sub-pseudo-Riemannian manifold and prove that the maximal dimension is attained for the left invariant structures on the Heisenberg group.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016072
Classification : 53C17, 34H05
Keywords: Contact structure, sub-Riemannian geometry, sub-Lorentzian geometry, Heisenberg group, isometry group, control-affine systems

Grochowski, Marek 1 ; Kryński, Wojciech 2

1 Faculty of Mathematics and Natural Sciences, Cardinal Wyszyński University, 01-938 Warszawa, Poland.
2 Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warszawa, Poland. 
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Grochowski, Marek; Kryński, Wojciech. On contact sub-pseudo-Riemannian isometries. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1751-1765. doi: 10.1051/cocv/2016072

A. Agrachev, Exponential mappings for contact sub-Riemannian structures. J. Dynam. Control Syst. 2 (1996) 321–356. | Zbl | MR | DOI

A. Agrachev, El.-H. Chakir, El.-A. and J.P. Gauthier, Sub-Riemannian metrics on R 3 . In vol. 25 of Canadian Mathematical Society Conference Proceedings (1998). | Zbl | MR

A. Agrachev and D. Barilari, Sub-Riemannian structures on 3D Lie groups. J. Dynam. Control Syst. 18 (2012) 21–44. | Zbl | MR | DOI

M. Gromov, Carnot-Carathéodory spaces seen from within. Sub-Riemannian geometry. In vol. 144 of Progr. Math. Birkhäuser, Basel (1996) 79–323. | Zbl | MR

M. Grochowski, The structure of reachable sets for affine control systems induced by generalized Martinet sub-Lorentzian metrics. ESAIM: COCV 18 (2012) 1150–1177. | Zbl | Numdam | MR

M. Grochowski, Remarks on global sub-Lorentzian geometry. Anal. Math. Phys. 3 (2013) 295–309. | Zbl | MR | DOI

M. Grochowski and W. Kryński, Invariants of Contact sub-pseudo-Riemannian Structures and Einstein-Weyl Geometry. Radon Ser. Comput. Appl. Math. 18 (2016). | Zbl | MR

M. Grochowski and B. Warhurst, Invariants and Infinitesimal Transformations for Contact Sub-Lorentzian Structures on 3-Dimensional Manifolds. SIGMA 11 (2015) 031. | Zbl | MR

E. Grong and A. Vasilev, Sub-Riemannian and sub-Lorentzian geometry on SU(1,1) and on its universal cover. J. Geom. Mech. 3 (2011) 225–260. | Zbl | MR | DOI

S. Kobayashi, Transformation groups in differential geometry. Springer-Verlag, New York, Heidelberg (1972). | Zbl | MR

A. Korolko and I. Markina, Geodesics on H-type quaternion groups with sub-Lorentzian metric and their physical interpretation. Complex Anal. Oper. Theory 4 (2010) 589–618. | Zbl | MR | DOI

B. Kruglikov, Finite-dimensionality in Tanaka theory. Ann. Inst. Henri Poincaré Anal. Non Linéaire 28 (2011) 75–90. | Zbl | Numdam | MR | DOI

B. Kruglikov, Symmetries of filtered structures via filtered Lie equations. J. Geom. Phys. 85 (2014) 164–170. | Zbl | MR | DOI

P. Lancaster and L. Rodman, Canonical forms for symmetric/skew-symmetric real matrix pairs under strict equivalence and congruence. Linear Algebra Appl. 406 (2005) 1–76. | Zbl | MR | DOI

R. Montgomery, A Tour of Subriemannian Geometries, Their Geodesics and Applications. In vol. 91 of Mathematical Surveys and Monographs. AMS (2006). | Zbl | MR

N. Tanaka, On differential systems, graded Lie algebras and pseudogroups. J. Math. Kyoto Univ. 10 (1970) 1–82 | Zbl | MR

R. Thompson, Pencils of Complex and Real Symmetric and Skew Matrices. Linear Algebra Appl. 147 (1991) 323–371. | Zbl | MR | DOI

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