1. (jointly with Zaifeng Lin) On Eisenhart's type theorem for sub-Riemannian metrics on step $2$ distributions with ad-surjective Tanaka symbols, Regular and Chaotic Dynamics, Springer, accepted for publication, arxiv version arXiv:2308.14218.
2. (Jointly with David Sykes) On geometry of 2-nondegenerate CR structures of hypersurface type and flag structures on leaf spaces of Levi foliations, Advances in Mathematics, Volume 413, published online on January 15, 2023, 65 pages, DOI 10.1016/j.aim.2022.108850, link to online journal version , arxiv version arXiv:2010.02770 [math.CV]
3. 1. (Jointly with David Sykes) Maximal
dimension of groups of symmetries of homogeneous 2-nondegenerate CR
structures of hypersurface type with a 1-dimensional Levi kernel, Transformation groups, published online, 30 pages, DOI 10.1007/s00031-022-09739-3, link to online journal version, extended version in arXiv:2102.08599[math.CV], 38 pages
4. (Jointly with Curtis Porter) Absolute parallelism for 2-nondegenerate CR structures via bigraded Tanaka prolongation, J. Reine Angew. Math. 777 (2021), 195--250. link to the journal online version 56 pages, preprint arXiv:1704.0399v3[math.DG], 44 pages.
5. (jointly with Yanhe Huang, George Petroulakis, and Frank Sottile) Nontrivial linear projections of the Grassmannian Gr_3(C^6), Linear Algebra Appl. 610 (2021), 488-505 , link to the journal online publication, arXiv:2004.10070 [math. AG] 14 pages.
6. (Jointly with Frederic Jean and Sofya Maslovskaya) On Weyl's type theorems and genericity of projective rigidity in sub-Riemannian Geometry, Geometriae Dedicata, Volume 213, 295-314, (2021) link to the journal online publication, 20 pages, arXiv:2001.08584v1 [math.DG]. 18 pages
7. (jointly with David Sykes) A canonical form for pairs consisting of a Hermitian form and a self-adjoint antilinear operator. Linear Algebra Appl. 590 (2020), 32–61, journal online version, arXiv:1909.09201v1[math,CV]
8. Canonical bundles of moving frames for parametrized curves in Lagrangian Grassmannians: algebraic approach, The
notes in almost the same form are included under my authorship as the
Appendix in the book "A Comprehensive Introduction to sub-Riemannian
Geometry from Hamiltonian view point"S by A. Agrachev D. Barilari, U.
Boscain. arXiv:1812.10501 [math.DG] 9. (Jointly with Frederic Jean and Sofya Maslovskaya) On projective and affine equivalence of sub-Riemannian metrics, Geometriae Dedicata, volume 203, 279-319(2019), journal online version , arXiv:1801.04257[math.DG], 38 pages. 10. (Jointly with Frederic Jean and Sofya Maslovskaya), Inverse Optimal Control Problem: the Sub-Riemannian Case, IFAC (International Federation of Automatic Control)-PapersOnLine, vol. 50, pp. 500--505, 2017. 11. (Jointly with Yanhe Huang and Frank Sottile) , Injectivity of generalized Wronski maps , Canad. Math. Bull. 60 (2017), no. 4, 747–761, pdf (revised journal version) 12. Control of nonholonomic systems: from sub-Riemannian geometry to motion planning [book review of MR3308372]. Bull. Amer. Math. Soc. (N.S.) 53 (2016), no. 1, 151–158. journal online version 13. (Jointly with Nickolas Hein and Frank Sottile) , A congruence modulo four for real Schubert calculus with isotropic flags, s. Canad. Math. Bull. 60 (2017), no. 2, 309–318. , pdf 14. (jointly with P.W.
Lee, C. Li) Ricci
curvature type lower bounds for
sub-Riemannian structures on Sasakian manifolds,
Discrete and Continuous Dynamical Systems - Series A, Volume 36,
Issue 1, 2016 Pages 303-321, arxiv version (entitled Measure contraction properties of 15. (Jointly with A. Sprintson and M. Yan) Weakly secure data exchange with Generalized Reed Solomon codes, 2014 IEEE International Symposium on Information Theory (ISIT), 2014, pp. 1366 - 1370. pdf 16. (Jointly with Boris Doubrov) Geometry
of rank 2 distributions with nonzero Wilczynski invariants,
J. Nonlinear Math. Phys. 21 (2014), no. 2, 166–187, link to the journal online version; longer version arXiv:1301.2797 v1[math. DG], 27 pages, pdf
17. (Jointly with Nickolas Hein and Frank Sottile) A congruence modulo four in real Schubert calculus, Journal fur die reine und angewandte Mathematik (Crelle), link to the journal online version; arXiv:1211.7160 v1 [math. AG], 24 pages. pdf 18. (Jointly with Boris Doubrov) Symmetries of trivial systems of ODEs of mixed order, Differential
Geometry and its Applications, 33 (2014), suppl., 123–143, link to the journal online version, arXiv:1302.7119
v1 [math. DG], 28 pages, pdf 19. (Jointly with Boris Doubrov) On geometry of affine control systems with one input , in the book `` Geometric Control Theory and sub-Riemannain Geometry'', G. Stefani, 20.
(Jointly with Boris Doubrov) Geometry of curves in generalized flag varieties , Transformation Groups, June 2013, Volume 18, Issue 2, pp 361-383, link to the journal online version , arXiv:1110.0226
v2 [math. DG], 28 pages arxiv version pdf ,
21.
(Jointly with Boris Doubrov) On geometry of curves of flags of constant
type, Cent. Eur. J. Math., 2012,
10(5), 1836-1871
DOI: 10.2478/s11533-012-0078-7 link to the journal online version ,
arXiv:1110.0242
v1 [math. DG], 39 pages .pdf (updated compared to the arxiv version)
22.
(Jointly with Boris Doubrov) Equivalence of Variational Problems of Higher
Order, Differential
Geometry and its Applications , Volume 29, Issue 2, March 2011, Pages 255-270 link to the journal online version , arXiv:1004.1730 [math.DG] arxiv version pdf
23.
(Jointly with Wojciech Krynski) Canonical frames for distributions of
odd rank and corank 2 with maximal first Kronecker index, Journal of
Lie Theory, 21 (2011), No. 2, 307--346 , link to the journal online version arXiv: 1003.1405 v1 [math.
DG] , arxiv version pdf
24.
(Jointly with Chengbo Li) Jacobi Equations and Comparison Theorems for Corank 1
sub-Riemannian Structures with Symmetries, Journal of Geometry and
Physics 61 (2011) 781-807,
link to the journal online version
contact sub-riemannian manifolds with symmetry), arXiv:1304.2658 v1 [math. DG], 29 pages, pdf
25. On Tanaka's prolongation procedure for filtered structures of constant type , Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Special Issue "Elie Cartan and Differential Geometry", v. 5, 2009, doi:10.3842/SIGMA.2009.094, 0906.0560 v3 [math.DG], 21 pages. link to the journal online version pdf
26. (Jointly with B. Doubrov)
On local geometry of nonholonomic rank 2 distributions, Journal of London Mathematical Society, 80(3):545-566, 2009, link to the journal online version doi:
10.1112/jlms/jdp044, arxiv
math.DG/0703662, 21 pages .arxiv version pdf
27. (Jointly with Chengbo Li) Differential geometry of curves in Lagrange Grassmannians with given Young diagram, Differential Geometry and its Applications, 27 (2009), 723-742, DOI: 10.1016/j.difgeo.2009.07.002 , link to the journal online version, arXiv:0708.1100v1 [math.DG], .arxiv version pdf
28. (Jointly with Chengbo Li) Parametrized curves in Lagrange Grassmannians,
C.R. Acad. Sci. Paris, Ser. I, Vol. 345, Issue 11, December 2007, 647-652,, link to the journal online version, .pdf 30.
(Jointly with A. Agrachev) Nurowski's conformal structures for
(2,5)-distributions via dynamics of abnormal extremals,
Proceedings of RIMS Symposium on "Developments of Cartan Geometry and
Related Mathematical Problems", "RIMS Kokyuroku" series 1502 (2006), pp 204-218, link to the series online version,
arxiv math.DG/0605059, 13 pages, .arxiv version pdf
31. (Jointly with B. Doubrov) A canonical frame for nonholonomic rank two distributions of maximal class, C.R. Acad. Sci. Paris, Ser. I, Vol. 342, Issue 8 (15 April 2006), 589-594, link to the journal online version, arxiv math.DG/0504319, SISSA preprint 25/2005/M .arxiv version pdf
32. On Variational Approach to Differential Invariants of Rank 2 Vector Distributions, Differential Geometry and Its Applications, Vol. 24, Issue 3 (May 2006), 235-259; link to the journal online version, arXiv:math/0402171 (the long version 37 pages) arxiv version pdf
33. Fundamental form and Cartan's tensor of (2,5)-distributions coincide, J. Dynamical and Control Systems, Vol.12, No. 2, April 2006, 247-276; link to the journal online version arxiv math. DG/0402195, SISSA preprint 13/2004/M, arxiv version pdf34. Complete systems of invariants for rank 1 curves
in
Lagrange Grassmannians, Differential Geom. Application, Proc. Conf.
Prague, 2005, pp 365-379, Charles University, Prague; arxiv math. DG/0411190, SISSA preprint 82/2004/M
.ps , pdf
35. On geodesic equivalence of Riemannian metrics and
sub-Riemannian metrics on distributions of corank 1, Journal of Mathematical Sciences, Vol. 135, Number 4 (June 2006),
3168 - 3194, link to the journal online version arxiv math. DG/0406111, SISSA preprint 41/2004/M, 30 pages..ps, .pdf
36. (Jointly with A. Agrachev and N. Chtcherbakova) On
curvatures and focal points
of dynamical Lagrangian distributions and their reductions by first
integrals, J. Dynamical and Control Systems, 11, 2005, No.3,
297-327. link to the journal online version arxiv math. DG/0409152, SISSA preprint 58/2004/M arxiv version pdf
37. (Jointly with A. Agrachev) Geometry of Jacobi curves.
I, J. Dynamical and Control Systems, 8, 2002, No. 1, 93-140.
.pdf
38. (Jointly with A. Agrachev) Geometry of Jacobi
curves. II, J. Dynamical and Control Systems, 8, 2002, No.2,
167-215. .pdf
39. (Jointly with A. Agrachev ) Principle Invariants of
Jacobi curves, In the book: Nonlinear Control in the Year 2000, v.1,A. Isidori, F.
Lamnabhi-Lagarrigue \&
W.Respondek, Eds, Lecture Notes in Control and Information Sciences
258, Springer, 2001, 9-22..pdf
40. Nonregular abnormal extremals of 2-distribution:
existence, second variation and rigidity, J. Dynamical and Control systems , 5(1999), No. 3, 347-383. .pdf
41. (Jointly with M.Zhitomirskii) Rigid paths of
generic 2-distributions on 3-manifolds, Duke Mathematical Journal, Vol. 79, No. 2, 1995, 281-307, .pdf