Mathematical Institute
Topic
Differential invariants
PhD. program
Mathematics (PF UPJŠ, Mathematics (1113))
Year of admission
2026
Name of the supervisor
doc. RNDr. Karol Nemoga, CSc.
Contact:
Receiving school
Faculty of Science, Pavol Jozef Šafárik University Košice
Annotation
supervisor: doc. RNDr. Ján Brajerčík, PhD., MI SAS, Košice (external supervisor),
e-mail: jan.brajercik@unipo.sk
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The thesis is based on the theory of differential invariants contained in the publication [1]. A focus of the thesis are differential invariants of tensors. The thesis also deals with the basic consequences of invariance in global variational geometry, such as conservation laws for extremal equations. The goal is to find assertions on the structure of all differential invariants of the metric and the given tensor field. The obtained results can be used for finding invariant Lagrangians for different types of physical fields.
References:
[1] D. Krupka, J. Janyška, Lectures on Differential Invariants, Folia Facultatis Scientiarum Naturalium Universitatis Purkynienae Brunensis, Mathematica 1, University J. E. Purkyně, Brno, 1990.
[2] D. Krupka, Introduction to Global Variational Geometry, Atlantis Studies in Variational Geometry, D. Krupka, H. Sun (Eds.), Atlantis Press, 2015.
[3] J. Brajerčík, Second order differential invariants of linear frames, Balkan J. Geom. Appl., Vol. 15, No. 2 (2010) 22-33 (electronic version).
e-mail: jan.brajercik@unipo.sk
==
The thesis is based on the theory of differential invariants contained in the publication [1]. A focus of the thesis are differential invariants of tensors. The thesis also deals with the basic consequences of invariance in global variational geometry, such as conservation laws for extremal equations. The goal is to find assertions on the structure of all differential invariants of the metric and the given tensor field. The obtained results can be used for finding invariant Lagrangians for different types of physical fields.
References:
[1] D. Krupka, J. Janyška, Lectures on Differential Invariants, Folia Facultatis Scientiarum Naturalium Universitatis Purkynienae Brunensis, Mathematica 1, University J. E. Purkyně, Brno, 1990.
[2] D. Krupka, Introduction to Global Variational Geometry, Atlantis Studies in Variational Geometry, D. Krupka, H. Sun (Eds.), Atlantis Press, 2015.
[3] J. Brajerčík, Second order differential invariants of linear frames, Balkan J. Geom. Appl., Vol. 15, No. 2 (2010) 22-33 (electronic version).