-
Previous Article
Groups of Lie type, vertex algebras, and modular moonshine
- ERA-MS Home
- This Volume
-
Next Article
Motivic functions, integrability, and applications to harmonic analysis on $p$-adic groups
Canonical Cartan connections on maximally minimal generic submanifolds $\mathbf{M^5 \subset \mathbb{C}^4}$
1. | Department of Pure Mathematics, University of Shahrekord, 88186-34141 Shahrekord, Iran |
2. | Département de Mathématiques d'Orsay, Bâtiment 425, Faculté des Sciences, F-91405 Orsay Cedex, France, France |
References:
[1] |
V. Beloshapka, V. Ezhov and G. Schmalz, Canonical Cartan connection and holomorphic invariants on Engel CR manifolds, Russian J. Mathematical Physics, 14 (2007), 121-133.
doi: 10.1134/S106192080702001X. |
[2] |
É. Cartan, Sur la géométrie pseudo-conforme des hypersurfaces de l'espace de deux variables complexes, II, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2), 1 (1932), 333-354. |
[3] |
J. Merker, Rationality in differential algebraic geometry, to appear in Proceedings of the Abel Symposium 2013, Springer Verlag, arXiv:1405.7625, 2013, 47 pp. |
[4] |
J. Merker, S. Pocchiola and M. Sabzevari, Equivalences of $5$-dimensional CR manifolds, I: General introduction, overview of results, and nonlinear computational aspects, http://arXiv.org, to appear. |
[5] |
J. Merker, S. Pocchiola and M. Sabzevari, Equivalences of $5$-dimensional CR manifolds, II: General classes $\sfI$, $\sf{II}$, $\sf{III}_{\sf{1}}$, $\sf{III}_{\sf{2}}$, $\sf{IV}_{\sf{1}}$, $\sf{IV}_{\sf{2}}$, arXiv:1311.5669, 95 pp. |
[6] |
J. Merker and M. Sabzevari, Explicit expression of Cartan's connections for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere, Cent. Eur. J. Math., 10 (2012), 1801-1835.
doi: 10.2478/s11533-012-0052-4. |
[7] |
J. Merker and M. Sabzevari, Cartan equivalences for $5$-dimensional CR-manifolds in $\mathbbC^4$ belonging to general class III, arXiv:1401.4297, 172 pp. |
[8] |
P. J. Olver, Equivalence, Invariants and Symmetry, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511609565. |
[9] |
S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964. |
show all references
References:
[1] |
V. Beloshapka, V. Ezhov and G. Schmalz, Canonical Cartan connection and holomorphic invariants on Engel CR manifolds, Russian J. Mathematical Physics, 14 (2007), 121-133.
doi: 10.1134/S106192080702001X. |
[2] |
É. Cartan, Sur la géométrie pseudo-conforme des hypersurfaces de l'espace de deux variables complexes, II, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2), 1 (1932), 333-354. |
[3] |
J. Merker, Rationality in differential algebraic geometry, to appear in Proceedings of the Abel Symposium 2013, Springer Verlag, arXiv:1405.7625, 2013, 47 pp. |
[4] |
J. Merker, S. Pocchiola and M. Sabzevari, Equivalences of $5$-dimensional CR manifolds, I: General introduction, overview of results, and nonlinear computational aspects, http://arXiv.org, to appear. |
[5] |
J. Merker, S. Pocchiola and M. Sabzevari, Equivalences of $5$-dimensional CR manifolds, II: General classes $\sfI$, $\sf{II}$, $\sf{III}_{\sf{1}}$, $\sf{III}_{\sf{2}}$, $\sf{IV}_{\sf{1}}$, $\sf{IV}_{\sf{2}}$, arXiv:1311.5669, 95 pp. |
[6] |
J. Merker and M. Sabzevari, Explicit expression of Cartan's connections for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere, Cent. Eur. J. Math., 10 (2012), 1801-1835.
doi: 10.2478/s11533-012-0052-4. |
[7] |
J. Merker and M. Sabzevari, Cartan equivalences for $5$-dimensional CR-manifolds in $\mathbbC^4$ belonging to general class III, arXiv:1401.4297, 172 pp. |
[8] |
P. J. Olver, Equivalence, Invariants and Symmetry, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511609565. |
[9] |
S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964. |
[1] |
Franz W. Kamber and Peter W. Michor. Completing Lie algebra actions to Lie group actions. Electronic Research Announcements, 2004, 10: 1-10. |
[2] |
Pengliang Xu, Xiaomin Tang. Graded post-Lie algebra structures and homogeneous Rota-Baxter operators on the Schrödinger-Virasoro algebra. Electronic Research Archive, 2021, 29 (4) : 2771-2789. doi: 10.3934/era.2021013 |
[3] |
Carlos Durán, Diego Otero. The projective Cartan-Klein geometry of the Helmholtz conditions. Journal of Geometric Mechanics, 2018, 10 (1) : 69-92. doi: 10.3934/jgm.2018003 |
[4] |
Waldyr M. Oliva, Gláucio Terra. Improving E. Cartan considerations on the invariance of nonholonomic mechanics. Journal of Geometric Mechanics, 2019, 11 (3) : 439-446. doi: 10.3934/jgm.2019022 |
[5] |
Boris Kalinin, Anatole Katok. Measure rigidity beyond uniform hyperbolicity: invariant measures for cartan actions on tori. Journal of Modern Dynamics, 2007, 1 (1) : 123-146. doi: 10.3934/jmd.2007.1.123 |
[6] |
Boris Kalinin, Anatole Katok, Federico Rodriguez Hertz. Errata to "Measure rigidity beyond uniform hyperbolicity: Invariant measures for Cartan actions on tori" and "Uniqueness of large invariant measures for $\Zk$ actions with Cartan homotopy data". Journal of Modern Dynamics, 2010, 4 (1) : 207-209. doi: 10.3934/jmd.2010.4.207 |
[7] |
Robert I. McLachlan, Ander Murua. The Lie algebra of classical mechanics. Journal of Computational Dynamics, 2019, 6 (2) : 345-360. doi: 10.3934/jcd.2019017 |
[8] |
Richard H. Cushman, Jędrzej Śniatycki. On Lie algebra actions. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : 1115-1129. doi: 10.3934/dcdss.2020066 |
[9] |
Tracy L. Payne. Anosov automorphisms of nilpotent Lie algebras. Journal of Modern Dynamics, 2009, 3 (1) : 121-158. doi: 10.3934/jmd.2009.3.121 |
[10] |
Javier Pérez Álvarez. Invariant structures on Lie groups. Journal of Geometric Mechanics, 2020, 12 (2) : 141-148. doi: 10.3934/jgm.2020007 |
[11] |
Anatole Katok, Federico Rodriguez Hertz. Uniqueness of large invariant measures for $\mathbb{Z}^k$ actions with Cartan homotopy data. Journal of Modern Dynamics, 2007, 1 (2) : 287-300. doi: 10.3934/jmd.2007.1.287 |
[12] |
Thierry Paul, David Sauzin. Normalization in Banach scale Lie algebras via mould calculus and applications. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4461-4487. doi: 10.3934/dcds.2017191 |
[13] |
Luca Capogna. Optimal regularity for quasilinear equations in stratified nilpotent Lie groups and applications. Electronic Research Announcements, 1996, 2: 60-68. |
[14] |
Gabriela P. Ovando. The geodesic flow on nilpotent Lie groups of steps two and three. Discrete and Continuous Dynamical Systems, 2022, 42 (1) : 327-352. doi: 10.3934/dcds.2021119 |
[15] |
Katarzyna Grabowska, Marcin Zając. The Tulczyjew triple in mechanics on a Lie group. Journal of Geometric Mechanics, 2016, 8 (4) : 413-435. doi: 10.3934/jgm.2016014 |
[16] |
Fang Li, Jie Pan. On inner Poisson structures of a quantum cluster algebra without coefficients. Electronic Research Archive, 2021, 29 (5) : 2959-2972. doi: 10.3934/era.2021021 |
[17] |
Mohammad Shafiee. The 2-plectic structures induced by the Lie bialgebras. Journal of Geometric Mechanics, 2017, 9 (1) : 83-90. doi: 10.3934/jgm.2017003 |
[18] |
Oǧul Esen, Hasan Gümral. Geometry of plasma dynamics II: Lie algebra of Hamiltonian vector fields. Journal of Geometric Mechanics, 2012, 4 (3) : 239-269. doi: 10.3934/jgm.2012.4.239 |
[19] |
Giovanni De Matteis, Gianni Manno. Lie algebra symmetry analysis of the Helfrich and Willmore surface shape equations. Communications on Pure and Applied Analysis, 2014, 13 (1) : 453-481. doi: 10.3934/cpaa.2014.13.453 |
[20] |
Hui-Ling Li, Heng-Ling Wang, Xiao-Liu Wang. A quasilinear parabolic problem with a source term and a nonlocal absorption. Communications on Pure and Applied Analysis, 2018, 17 (5) : 1945-1956. doi: 10.3934/cpaa.2018092 |
2020 Impact Factor: 0.929
Tools
Metrics
Other articles
by authors
[Back to Top]