Differential invariants of Lie pseudogroups

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https://hdl.handle.net/10037/15600
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Thesis introduction and papers I, III, IV, V and VI (PDF)
Entire thesis in one comprehensive file (PDF)
Date
2019-05-10
Type
Doctoral thesis
Doktorgradsavhandling

Author
Schneider, Eivind
Abstract
We compute differential invariants for several Lie pseudogroups, and use them for solving the equivalence and classification problem for a variety of mathematical structures appearing in geometry and mathematical physics. We demonstrate utility of the algebra of rational scalar differential invariants for solving these two problems, also in cases where the structures are given as solutions to a nonlinear partial differential equation and the Lie pseudogroup is infinite-dimensional. In addition to contributing to the study of important mathematical structures, our work brings new insight into the general theory of differential invariants.
Has part(s)

Paper I: Schneider, E. (2018). Projectable Lie algebras of vector fields in 3D. Journal of Geometry and Physics, 132, 222-229. Also available in Munin at https://hdl.handle.net/10037/14569.

Paper II: Schneider, E. Differential invariants of surfaces. (Manuscript). Available in the file “thesis_entire.pdf”.

Paper III: Kruglikov, B. & Schneider, E. (2017). Differential invariants of self-dual conformal structures. Journal of Geometry and Physics, 113, 176-187. Also available at https://doi.org/10.1016/j.geomphys.2016.05.017. Accepted manuscript version available in Munin at https://hdl.handle.net/10037/15607.

Paper IV: Kruglikov, B. & Schneider, E. (2018). Differential invariants of Einstein-Weyl structures in 3D. Journal of Geometry and Physics, 131, 160-169. Also available in Munin at https://hdl.handle.net/10037/15058.

Paper V: Kruglikov, B., McNutt, D. & Schneider, E. (2019). Differential invariants of Kundt waves. (Submitted manuscript). Accepted manuscript version available at https://iopscience.iop.org/article/10.1088/1361-6382/ab28c5.

Paper VI: Schneider, E. (2019). Differential invariants in thermodynamics. (Submitted manuscript). Published version in Kycia, R., Ułan, M. & Schneider, E. (Eds). Nonlinear PDEs, Their Geometry, and Applications. Tutorials, Schools, and Workshops in the Mathematical Sciences. Birkhäuser, Cham, available at https://doi.org/10.1007/978-3-030-17031-8_7.

Publisher
UiT Norges arktiske universitet
UiT The Arctic University of Norway
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