References
- V. Arnold, Sur la g´eom´etrie diff´erentielle des groupes de Lie de dimension infinie et ses applications ‘a l’hydrodynamique des fluides parfaits, Ann. Inst. Fourier Grenoble 16 (1966), 319–361.
- G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, 2012.
- M. Bauer, M. Bruveris, P. W. Michor, Overview of the geometries of shape spaces and diffeomorphism groups. J. Math. Imaging Vision 50 (2014), 60–97.
- I. Ciuclea, Nonlinear Grassmannians and their generalizations, doctoral dissertation, West University of Timisoara, 2024.
- I. Ciuclea, A. B. Tumpach, C. Vizman, Shape spaces of nonlinear flags, Proc. GSI 2023: Geometric Science of Information, Lecture Notes in Computer Science, ed. F. Nielsen and F. Barbaresco (2023), 44–50.
- I. Ciuclea, C. Vizman, Pointed vortex loops in ideal 2D fluids, J. Phys. A: Math. Theor. 56, 245201 (2023) (15pp).
- K. Conrad, Dihedral Groups II., Expository Papers, pusblished online at https://kconrad.math.uconn.edu/blurbs/grouptheory/dihedral2.pdf.
- F. Gay-Balmaz, C. Vizman, Isotropic submanifolds and coadjoint orbits of the Hamiltonian group, J. Symp. Geom. 17 (3) (2019), 663–702.
- F. Gay-Balmaz, C. Vizman, Coadjoint orbits of vortex sheets in ideal fluids, J. Geom. Phys. 197 (2024), Paper No. 105096, 13 pp.
- G. A. Goldin, R. Menikoff, D. H. Sharp, Diffeomorphism groups and quantized vortex filaments, Phys. Rev. Lett. 58 (1987), 2162–2164.
- S. Haller, C. Vizman, Non-linear Grassmannians as coadjoint orbits, Math. Ann. 329 (2004), 771–785.
- S. Haller, C. Vizman, Non-linear flag manifolds as coadjoint orbits, Ann. Global Anal. Geom. 58 (2020), 385–413.
- S. Haller, C. Vizman, A dual pair for the contact group. Math. Z. 301 (2022), 2937–2973.
- S. Haller, C. Vizman, Weighted non-linear flag manifolds as coadjoint orbits, Canadian Journal of Mathematics, published online (2023), 1-31.
- I. H. Jermyn, S. Kurtek, H. Laga, A. Srivastava, Elastic shape analysis of three-dimensional objects. Synth. Lect. Comput. Vision 12 (2017), 1–185.
- B. Khesin, Symplectic structures and dynamics on vortex membranes, Moscow Math. J. 12 (2013), 413–434.
- B. Lee, Geometric structures on spaces of weighted submanifolds, SIGMA 5 099 (2009), 46 pages.
- J. M. Lee, Introduction to Smooth Manifolds, Graduate Texts in Mathematics 218, Springer, 2013.
- J. E. Marsden, A. Weinstein, Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids, Phys. D 7 (1983), 305–323.
- P. W. Michor, Manifolds of mappings and shapes. In The legacy of Bernhard Riemann after one hundred and fifty years. Vol. II, 459–486, Adv. Lect. Math. 35.2, Int. Press, Somerville, MA, 2016.
- P. W. Michor, Manifolds of mappings for continuum mechanics. In: Segev, R., Epstein, M. (eds.) Geometric Continuum Mechanics. Advances in Mechanics and Mathematics vol. 42, pp. 3–75, Birkh¨auser, Basel, 2020.
- J. Strait, S. Kurtek, E. Bartha, S. N. MacEachern, Landmark-constrained elastic shape analysis of planar curves. J. Amer. Statist. Assoc. 112 (2017), 521–533.
- C. Vizman, Induced differential forms on manifolds of functions, Archivum Mathematicum 47 (2011), 201–215.
- A. Weinstein, Connections of Berry and Hannay type for moving Lagrangian submanifolds, Adv. Math. 82 (1990), 133–159.
