HR job title
- Professor
- Contact Info
- 1 979 845 5837
- Websites
- ORCiD
- 0000-0001-7900-2567
Zelenko, Igor Professor
Positions
- Professor, The Texas A&M University System
The main direction of my current research is the construction of canonical frames and differential invariants for a wide class of geometric structures and control systems on manifolds.
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- Works By Students
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Overview
Publications
selected publications
-
academic article
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Sykes, D., & Zelenko, I.
(2023).
On geometry of 2-nondegenerate CR structures of hypersurface type and flag structures on leaf spaces of Levi foliations. Advances in Mathematics.
413, 108850-108850.
-
Sykes, D., & Zelenko, I.
(2022).
Maximal Dimension of Groups of Symmetries of Homogeneous 2-nondegenerate CR Structures of Hypersurface Type with a 1-dimensional Levi Kernel. Transformation Groups.
1-38.
-
Jean, F., Maslovskaya, S., & Zelenko, I.
(2021).
On Weyl's type theorems and genericity of projective rigidity in sub-Riemannian geometry. Geometriae Dedicata.
213(1), 295-314.
-
Porter, C., & Zelenko, I.
(2021).
Absolute parallelism for 2-nondegenerate CR structures via bigraded Tanaka prolongation. Journal für die Reine und Angewandte Mathematik.
777(777), 195-250.
-
Huang, Y., Petroulakis, G., Sottile, F., & Zelenko, I.
(2021).
Nontrivial linear projections on the Grassmannian Gr(3)(C-6). Linear Algebra and Its Applications.
610, 488-505.
-
Sykes, D., & Zelenko, I.
(2021).
Maximal dimension of groups of symmetries of homogeneous 2-nondegenerate CR structures of hypersurface type with a 1-dimensional Levi kernel
-
Sykes, D., & Zelenko, I.
(2020).
On geometry of $2$-nondegenerate CR structures of hypersurface type and flag structures on leaf spaces of Levi foliations
-
Doubrov, B., & Zelenko, I.
(2020).
Vector distributions with very large symmetries via rational normal curves
-
Sykes, D., & Zelenko, I.
(2020).
A canonical form for pairs consisting of a Hermitian form and a self-adjoint antilinear operator. Linear Algebra and Its Applications.
590, 32-61.
-
Jean, F., Maslovskaya, S., & Zelenko, I.
(2019).
On projective and affine equivalence of sub-Riemannian metrics. 203(1), 279-319.
-
Zelenko, I.
(2018).
Canonical bundles of moving frames for parametrized curves in Lagrangian Grassmannians: algebraic approach
-
Huang, Y., Sottile, F., & Zelenko, I.
(2017).
Injectivity of Generalized Wronski Maps. Canadian Mathematical Bulletin.
60(4), 747-761.
-
Arefizadeh, S., Talebpour, A., & Zelenko, I.
(2017).
Platooning in the Presence of a Speed Drop: A Generalized Control Model. abs/1709.10083.
-
Hein, N., Sottile, F., & Zelenko, I.
(2017).
A Congruence Modulo Four for Real Schubert Calculus with Isotropic Flags. Canadian Mathematical Bulletin.
60(2), 309-318.
-
Jean, F., Maslovskaya, S., & Zelenko, I.
(2017).
Inverse Optimal Control Problem: the Sub-Riemannian Case. IFAC-PapersOnLine.
50(1), 500-505.
-
Doubrov, B., & Zelenko, I.
(2016).
On local geometry of vector distributions with given Jacobi symbols
-
Hein, N., Sottile, F., & Zelenko, I.
(2016).
A congruence modulo four in real Schubert calculus. Journal für die Reine und Angewandte Mathematik.
714(714), 151-174.
-
Lee, P., Li, C., & Zelenko, I.
(2016).
RICCI CURVATURE TYPE LOWER BOUNDS FOR SUB-RIEMANNIAN STRUCTURES ON SASAKIAN MANIFOLDS. Discrete and Continuous Dynamical Systems Series A.
36(1), 303-321.
-
Zelenko, I.
(2015).
Book Review: Control of nonholonomic systems: from sub-Riemannian geometry to motion planning. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
53(1), 151-158.
-
Doubrov, B., & Zelenko, I.
(2014).
Geometry of rank 2 distributions with nonzero Wilczynski invariants. Journal of Nonlinear Mathematical Physics.
21(2), 166-187.
-
Doubrov, B., & Zelenko, I.
(2014).
Symmetries of trivial systems of ODEs of mixed order. Differential Geometry and Its Applications.
33, 123-143.
-
Doubrov, B., & Zelenko, I.
(2013).
Geometry of curves in generalized flag varieties. Transformation Groups.
18(2), 361-383.
-
Doubrov, B., & Zelenko, I.
(2013).
Geometry of rank 2 distributions with nonzero Wilczynski invariants and affine control systems with one input
-
Doubrov, B., & Zelenko, I.
(2012).
Prolongation of quasi-principal frame bundles and geometry of flag structures on manifolds
-
Doubrov, B., & Zelenko, I.
(2012).
On geometry of curves of flags of constant type. Central European Journal of Mathematics.
10(5), 1836-1871.
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Krynski, W., & Zelenko, I.
(2011).
Canonical Frames for Distributions of Odd Rank and Corank 2 with Maximal First Kronecker Index. JOURNAL OF LIE THEORY.
21(2), 307-346.
-
Doubrov, B., & Zelenko, I.
(2011).
Equivalence of variational problems of higher order. Differential Geometry and Its Applications.
29(2), 255-270.
-
Li, C., & Zelenko, I.
(2011).
Jacobi equations and Comparison Theorems for corank 1 sub-Riemannian structures with symmetries. Journal of Geometry and Physics.
61(4), 781-807.
-
Doubrov, B., & Zelenko, I.
(2009).
On local geometry of non-holonomic rank 2 distributions. Journal of London Mathematical Society.
80(3), 545-566.
-
Zelenko, I.
(2009).
On Tanaka's Prolongation Procedure for Filtered Structures of Constant Type. Symmetry, Integrability and Geometry: Methods and Applications.
5, 21.
-
Zelenko, I., & Li, C.
(2009).
Differential geometry of curves in Lagrange Grassmannians with given Young diagram. Differential Geometry and Its Applications.
27(6), 723-742.
-
Doubrov, B., & Zelenko, I.
(2008).
On local geometry of rank 3 distributions with 6-dimensional square
-
Zelenko, I., & Li, C.
(2007).
Parametrized curves in lagrange grassmannians. COMPTES RENDUS MATHEMATIQUE.
345(11), 647-652.
-
Agrachev, A., & Zelenko, I.
(2007).
On feedback classification of control-affine systems with one- and two-dimensional inputs. SIAM Journal of Control and Optimization.
46(4), 1431-1460.
-
Agrachev, A., & Zelenko, I.
(2006).
Nurowski's conformal structures for (2,5)-distributions via dynamics of abnormal extremals
-
Doubrov, B., & Zelenko, I.
(2006).
A canonical frame for nonholonomic rank two distributions of maximal class. 342(8), 589-594.
-
Zelenko, I.
(2006).
Fundamental form and the Cartan tensor of (2,5)-distributions coincide. Journal of Dynamical and Control Systems.
12(2), 247-276.
-
Zelenko, I.
(2006).
On geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1. Journal of Mathematical Sciences: a translation of selected Russian-language serial publications in mathematics.
135(4), 3168-3194.
-
Zelenko, I.
(2006).
On variational approach to differential invariants of rank two distributions. Differential Geometry and Its Applications.
24(3), 235-259.
-
Agrachev, A. A., Chtcherbakova, N. N., & Zelenko, I.
(2005).
On curvatures and focal points of dynamical Lagrangian distributions and their reductions by first integrals. Journal of Dynamical and Control Systems.
11(3), 297-327.
-
Zelenko, I.
(2004).
Complete systems of invariants for rank 1 curves in Lagrange Grassmannians
-
Agrachev, A., & Zelenko, I.
(2002).
Geometry of Jacobi curves. II. Journal of Dynamical and Control Systems.
8(2), 167-215.
-
Agrachev, A. A., & Zelenko, I.
(2002).
Geometry of Jacobi curves. I. Journal of Dynamical and Control Systems.
8(1), 93-140.
-
Zelenko, I.
(1999).
Nonregular Abnormal Extremals of 2-Distribution: Existence, Second Variation, and Rigidity. Journal of Dynamical and Control Systems.
5(3), 347-383.
-
ZELENKO, I., & ZHITOMIRSKII, M.
(1995).
RIGID PATHS OF GENERIC 2-DISTRIBUTIONS ON 3-MANIFOLDS. DUKE MATHEMATICAL JOURNAL.
79(2), 281-307.
-
Sykes, D., & Zelenko, I.
(2023).
On geometry of 2-nondegenerate CR structures of hypersurface type and flag structures on leaf spaces of Levi foliations. Advances in Mathematics.
413, 108850-108850.
-
conference paper
-
Doubrov, B., & Zelenko, I.
(2014).
On geometry of affine control systems with one input. Springer INdAM Series.
133-152.
-
Yan, M., Sprintson, A., & Zelenko, I.
(2014).
Weakly Secure Data Exchange with Generalized Reed Solomon Codes. IEEE International Symposium on Information Theory - Proceedings.
1366-1370.
-
Agrachev, A., & Zelenko, I.
(2000).
Principal invariants of Jacobi curves. Lecture Notes in Control and Information Sciences.
9-21.
-
Doubrov, B., & Zelenko, I.
(2014).
On geometry of affine control systems with one input. Springer INdAM Series.
133-152.
-
institutional repository document
-
Lin, Z., & Zelenko, I.
(2023).
On Eisenhart's type theorem for sub-Riemannian metrics on step $2$ distributions with $mathrm{ad}$-surjective Tanaka symbols
-
Berkolaiko, G., & Zelenko, I.
(2023).
Morse inequalities for ordered eigenvalues of generic self-adjoint families
-
Sykes, D., & Zelenko, I.
(2021).
Maximal dimension of groups of symmetries of homogeneous 2-nondegenerate CR structures of hypersurface type with a 1-dimensional Levi kernel
-
Sykes, D., & Zelenko, I.
(2020).
On geometry of $2$-nondegenerate CR structures of hypersurface type and flag structures on leaf spaces of Levi foliations
-
Huang, Y., Petroulakis, G., Sottile, F., & Zelenko, I.
(2020).
Nontrivial linear projections of the Grassmannian Gr_3(C^6)
-
Doubrov, B., & Zelenko, I.
(2020).
Vector distributions with very large symmetries via rational normal curves
-
Jean, F., Maslovskaya, S., & Zelenko, I.
(2020).
On Weyl's type theorems and genericity of projective rigidity in sub-Riemannian Geometry
-
Sykes, D., & Zelenko, I.
(2019).
A canonical form for pairs consisting of a Hermitian form and a self-adjoint antilinear operator
-
Zelenko, I.
(2018).
Canonical bundles of moving frames for parametrized curves in Lagrangian Grassmannians: algebraic approach
-
Jean, F., Maslovskaya, S., & Zelenko, I.
(2018).
On projective and affine equivalence of sub-Riemannian metrics
-
Arefizadeh, S., Talebpour, A., & Zelenko, I.
(2017).
Platooning in the Presence of a Speed Drop: A Generalized Control Model
-
Porter, C., & Zelenko, I.
(2017).
Absolute parallelism for 2-nondegenerate CR structures via bigraded Tanaka prolongation
-
Doubrov, B., & Zelenko, I.
(2016).
On local geometry of vector distributions with given Jacobi symbols
-
Huang, Y., Sottile, F., & Zelenko, I.
(2016).
Injectivity of generalized Wronski maps
-
Hein, N., Sottile, F., & Zelenko, I.
(2014).
A congruence modulo four in real Schubert calculus with isotropic flags
-
Lee, P., Li, C., & Zelenko, I.
(2013).
Ricci curvature type lower bounds for sub-Riemannian structures on Sasakian manifolds
-
Doubrov, B., & Zelenko, I.
(2013).
Symmetries of trivial systems of ODEs of mixed order
-
Hein, N., Sottile, F., & Zelenko, I.
(2012).
A congruence modulo four in real Schubert calculus
-
Doubrov, B., & Zelenko, I.
(2011).
Geometry of curves in parabolic homogeneous spaces
-
Doubrov, B., & Zelenko, I.
(2011).
On geometry of curves of flags of constant type
-
Doubrov, B., & Zelenko, I.
(2010).
Equivalence of variational problems of higher order
-
Krynski, W., & Zelenko, I.
(2010).
Canonical frames for distributions of odd rank and corank 2 with maximal first Kronecker index
-
Li, C., & Zelenko, I.
(2009).
Jacobi Equations and Comparison Theorems for Corank 1 sub-Riemannian Structures with Symmetries
-
Zelenko, I.
(2009).
On Tanaka's Prolongation Procedure for Filtered Structures of Constant Type
-
Zelenko, I., & Li, C.
(2007).
Differential geometry of curves in Lagrange Grassmannians with given Young diagram
-
Doubrov, B., & Zelenko, I.
(2007).
On local geometry of nonholonomic rank 2 distributions
-
Doubrov, B., & Zelenko, I.
(2005).
A Canonical Frame for Nonholonomic Rank Two Distributions of Maximal Class
-
Agrachev, A., & Zelenko, I.
(2005).
On feedback classification of control-affine systems with one and two-dimensional inputs
-
Agrachev, A. A., Chtcherbakova, N. N., & Zelenko, I.
(2004).
On curvatures and focal points of dynamical Lagrangian distributions and their reductions by first integrals
-
Zelenko, I.
(2004).
On geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1
-
Zelenko, I.
(2004).
Variational Approach to Differential Invariants of Rank 2 Vector Distributions
-
Zelenko, I.
(2004).
Fundamental form and Cartan's tensor of (2,5)-distributions coincide
-
Lin, Z., & Zelenko, I.
(2023).
On Eisenhart's type theorem for sub-Riemannian metrics on step $2$ distributions with $mathrm{ad}$-surjective Tanaka symbols
Research
principal investigator on
co-principal investigator on
Teaching
teaching activities
- MATH251 Engineering Math Iii Instructor
- MATH308 Differential Equations Instructor
- MATH308 Differential Equations Instructor
- MATH485 Hnr-directed Studies Instructor
- MATH491 Hnr-research Instructor
- MATH622 Differential Geometry I Instructor
- MATH623 Differential Geometry Ii Instructor
- MATH666 Seminar In Geometry Instructor
- MATH684 Prof Internship Instructor
- MATH685 Directed Studies Instructor
- MATH689 Sptp: Physics-mathematicians Instructor
- MATH691 Research Instructor
Works By Students
chaired theses and dissertations
-
Huang, Yanhe (2016-05). Injectivity Properties of Generalized Wronski Map.
-
Porter, Curtis Wade (2016-06). The Local Equivalence Problem for 7-dimensional, 2-nondegenerate CR Manifolds whose Cubic Form is of Conformal Unitary Type.
-
Wendel, Eric Duong Ba (2015-07). On the Maximality of Class of Rank-2 Distributions with 5-Dimensional Cube.
Background
education and training
- Ph.D. in Mathematics, Technion - Israel Institute of Technology - (Haifa, Israel) 2002
- M.S. in Mathematics, Technion - Israel Institute of Technology - (Haifa, Israel) 1998
- B.A. in Mathematics, Technion - Israel Institute of Technology - (Haifa, Israel) 1994
Contact
first name
- Igor
has last name
- Zelenko
mailing address
-
Texas A&M University
Mathematics
3368 TAMU
College Station, TX 77843-3368
USA
Other
- zelenkotamu@tamu.edu