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Publications

The recent publication record of members of the LRI includes:

2021

• D. Krupka, Higher-order homogeneous functions: Classification, Publ. Math. Debrecen (2021), to appear
• D.J. Saunders, Jets and the variational calculus, Comm. Math. 29 (2021) 91-114
• Z Urban, J Volná, On the Carathéodory Form in Higher-Order Variational Field Theory, Symmetry 13 (5), 800
• EN Saridakis, R Lazkoz, V Salzano, PV Moniz, S Capozziello, JB Jiménez,…, Modified Gravity and Cosmology: An Update by the CANTATA Network, arXiv preprint arXiv:2105.12582
• N Minculete, C Pfeifer, N Voicu, Inequalities from Lorentz-Finsler norms, Mathematical Inequalities & Applications 24 (2), 373–398
• N Voicu, S Garoiu, B Vasian, On the closure property of Lepage equivalents of Lagrangians, https://arxiv.org/abs/2102.12955
• M Hohmann, C Pfeifer, N Voicu, Canonical variational completion and 4D Gauss-Bonnet gravity,, Eur. Phys. J. Plus 136 (180)

2020

• D. Krupka, Variational principles: Projectability onto Grassmann fibrations, J. Math. Phys. 61, 123501 (2020)
• Z Urban, F Bajardi, S Capozziello, The Noether Bessel Hagen Symmetry Approach for Dynamical Systems, Int. J. Geom. Methods Mod. Phys. 17 (2020) 14, 2050215
• M Hohmann, C Pfeifer, N Voicu, The kinetic gas universe, Eur. Phys. J. C 80 (2020) 9, 809
• M Hohmann, C Pfeifer, N Voicu, Cosmological Finsler Spacetimes, Universe 6 (5), 65
• A Fuster, S Heefer, C Pfeifer, N Voicu, On the non metrizability of Berwald Finsler spacetimes, Universe 6 (5), 64
• M Hohmann, C Pfeifer, N Voicu, Relativistic kinetic gases as direct sources of gravity, Phys. Rev. D 101 (2), 024062
• V. Gakis, M. Krššák, J. L. Said, E. N. Saridakis, Conformal Gravity and Transformations in the Symmetric Teleparallel Framework, Phys. Rev. D 101 (2020) 6, 064024

2019

• D. Krupka, Variational forces, Journal of Mathematical Sciences (2019), in print
• D. Krupka, Lepage forms in Finsler geometry: 2nd-order generalization, Int. J. of Geom. Methods  Mod. Phys. 16, 1941005 (2019)
• Z Urban, J Volná, Exactness of Lepage 2-forms and globally variational differential equations,  Int. J. Geom. Methods Mod. Phys. 16, No. 02 (2019) 1950106
• Z Urban, J Volná, On a global Lagrangian construction for ordinary variational equations on 2-manifolds, J. Math. Phys. 60, 092902 (2019)
• M Hohmann, C Pfeifer, N Voicu, Finsler gravity action from variational completion, Phys. Rev. D 100 (6), 064035
• M. Hohmann, L. Järv, M. Krššák, Ch. Pfeifer, Modified teleparallel theories of gravity in symmetric spacetimes, Phys. Rev. D 100 (2019) 8, 084002
• L. Järv, M. Hohmann, M. Krššák, Ch. Pfeifer, Flat connection for rotating spacetimes in extended teleparallel gravity theories, Universe 5 (2019) 142
• M. Krššák, R. J. van Den Hoogen, J. G. Pereira, C. G. Boehmer, A. A. Coley, Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach, Class. Quant. Grav. 36 (2019) 18, 183001

2018

• D. Krupka, Z. Urban, J. Volna, Variational submanifolds of Euclidean spaces, J. Math. Phys. 59, 032903 (2018)
• D.J. Saunders, On Lagrangians with reduced-order Euler-Lagrange equations, SIGMA 14 (2018) 089
  
• Z Urban, J Brajerčík, The fundamental Lepage form in variational theory for submanifolds,  Int. J. Geom. Methods Mod. Phys. 15 (06), 1850103
• N Voicu, Conformal maps between pseudo-Finsler spaces, Int. J. Geom. Methods Mod. Phys. 15 (01), 185000
• M. Hohmann, L. Järv, M. Krššák, Ch. Pfeifer, Propagation of gravitational waves in teleparallel gravity theories, Phys. Rev. D 98 (2018) 12, 124004
• M. Hohmann, L. Järv, M. Krššák, Ch. Pfeifer, Teleparallel theories of gravity as analogue of nonlinear electrodynamics, Phys. Rev. D 97 (2018) 10, 104042
• S. Capozziello, K. F. Dialektopoulos, O. Luongo, Maximum turnaround radius in $f(R)$ gravity, Int. J. Mod. Phys. D 28 (2018) no.03, 1950058 
• M. Benetti, S. Santos da Costa, S. Capozziello, J. S. Alcaniz, M. De Laurentis, Observational constraints on Gauss-Bonnet cosmology, Int. J. Mod. Phys. D 27 (2018) no.08, 1850084

2017

• D.J. Saunders, Vertical symmetries of Cartan geometries, Diff. Geom. Appl. 54 (2017), 165-174
• J Brajercík, Z Urban, On homogeneous functions in second-order field theory, Syst. Wspomagania Inz. Prod. 6
• Z Urban, J Volna, Variational equations on the Möbius strip, Syst. Wspomagania Inz. Prod. 6
• N Voicu, Volume forms for time orientable Finsler spacetimes,  J. Geom. Phys. 12 (February 2017), 85-94
• S. Bahamonde, Ch. Boehmer, M. Krššák, New classes of modified teleparallel gravity models, Phys. Lett. B 775 (2017) 37–43,

2016

• G. Sardanashvily, Noether's Theorems, Applications in Mechanics and Field Theory, Atlantis Studies in Variational Geometry, Vol. 3, Atlantis Press, Amsterdam-Beijing-Paris, 2016.
• N. Voicu, Energy–momentum tensors in classical field theories - A modern perspective, Int. J. Geom. Meth. Mod. Phys. (2016) in print.
• Z. Urban and J. Volna, The metrizability problem for Lorentz-invariant affine connections, Int. J. Geom. Meth. Mod. Phys., vol. 13, no. 8, (2016)
• A.V. Zhuchok and M. Demko, Free n-dinilpotent doppelsemigroups, in: Algebra and Discrete Mathematics, Vol. 22, no. 2 (2016), pp. 304-316.

2015

• A.M. Bloch, D. Krupka, and D.V. Zenkov, The Helmholtz Conditions and the Method of Controlled Lagrangians, in: D. Zenkov (Ed.), The Inverse Problem of the Calculus of Variations, Atlantis Press, Amsterdam-Beijing-Paris, 2015, pp. 1-29.
• D. Krupka, The Sonin-Douglas Problem, in: D. Zenkov (Ed.), The Inverse Problem of the Calculus of Variations, Atlantis Press, Amsterdam-Beijing-Paris, 2015, pp. 31-73.
• J. Volná and Z. Urban, First-order Variational Sequences in Field Theory, in: D. Zenkov (Ed.), The Inverse Problem of the Calculus of Variations, Atlantis Press, Amsterdam-Beijing-Paris, 2015, pp. 215-284.
• R. Matsyuk, Inverse Variational Problem and Symmetry in Action: The Relativistic Third Order Dynamics, in: D. Zenkov (Ed.), The Inverse Problem of the Calculus of Variations, Atlantis Press, Amsterdam-Beijing-Paris, 2015, pp. 75-102.
• N. Voicu, Source Forms and Their Variational Completions, in: D. Zenkov (Ed.), The Inverse Problem of the Calculus of Variations, Atlantis Press, Amsterdam-Beijing-Paris, 2015, pp. 171-214.
• Z. Urban, Variational Principles for Immersed Submanifolds, in: D. Zenkov (Ed.), The Inverse Problem of the Calculus of Variations, Atlantis Press, Amsterdam-Beijing-Paris, 2015, pp. 103-170.
• J. Volna and Z. Urban, The interior Euler-Lagrange operator in field theory, Math. Slovaca 65, No. 6 (2015) 1427-1444.
  DOI: 10.1515/ms-2015-0097
• N. Voicu and D. Krupka, Canonical variational completions of differential systems, J. Math. Phys. 56, 043507 (2015); arXiv:1406.6646 [math-ph].  
• D. Krupka, G. Moreno, Z. Urban, J. Volná, On a bicomplex induced by the variational sequence, Int. J. Geom. Meth. Mod. Phys. 12, No. 5 (2015) 1550057 (15 pp.) DOI: 10.1142/S0219887815500577
• G. Moreno and M.E. Stypa, Natural boundary conditions in geometric calculus of variations, Math. Slovaca 65, No. 6 (2015), 1531-1556, DOI: 10.1515/ms-2015-0105
• Z. Urban and D. Krupka, Variational theory on Grassmann fibrations: Examples, Acta Math. Acad. Paed. Nyíregyhasiensis 31, No. 1 (2015) 153-170.  pdf
• D. Krupka, Invariant variational structures on fibered manifolds, Int. J. Geom. Met. Mod. Phys. 12, No. 2 (2015) 1550020.
• D. Krupka, Introduction to Global Variational Geometry, Atlantis Studies in Variational Geometry, Vol. 1, Atlantis Press, Amsterdam-Beijing-Paris, 2015.

2014

• Z. Urban and D. Krupka, Foundations of higher-order variational theory on Grassmann fibrations, Int. J. Geom. Met. Mod. Phys. 11, No. 7 (2014) 1460023 (27 pp.) doi 
• N. Voicu, Biharmonic maps from Finsler spaces, Publicationes Mathematicae Debrecen 84, No. 3-4 (2014). 
• J. Brajercik, M. Demko and D. Krupka, Principal bundle structure on jet prolongations of frame bundles, Math. Slovaca 64, No. 5 (2014) 1277-1290.

• J. Brajercik and M. Demko, On sheaf spaces of partially ordered quasigroups, Quasigroups and Related Systems 22 (2014) 51-58.

• D. Krupka, Lepage forms in Kawaguchi spaces and the Hilbert form, paper in honor of Professor Lajos Tamassy, Publ. Math. Debrecen 84, No. 1-2 (2014) 147-164.

2013

• J. Brajercik and M. Demko, Second order natural Lagrangians on coframe bundles, Miskolc Mathematical Notes 14, No. 2 (2013), 487-494.  pdf
• D. Krupka, Z. Urban and J. Volna, Variational projectors in fibred manifolds, Miskolc Mathematical Notes 14, No. 2 (2013), 503-516.  pdf
• E. Tanaka and D. Krupka, On the structure of Finsler and Areal spaces, Miskolc Mathematical Notes 14, No. 2 (2013), 539-546.  pdf
• Z. Urban and D. Krupka, The Helmholtz conditions for systems of second order homogeneous differential equations, Publ. Math. Debrecen (2013), 83, No. 1-2 (2013) 71-84.
• T. Li and D. Krupka, The geometry of tangent bundles: Canonical vector fields, Geometry (2013), Hindawi Publishing Corporation, Article ID 364301, 10 pp.  doi-pdf
• Z. Urban and D. Krupka, The Zermelo conditions and higher order homogeneous functions, Publ. Math. Debrecen 82, No. 1 (2013) 59-76.

2012

• M. Demko, Partially ordered quasigroups, Southeast Asian Bulletin of Mathematics 36 (5), (2012), 631–649. 
• Z. Urban and D. Krupka, Variational sequences on fibred velocity spaces, Glob. J. Math. Sci. 1, No. 1, 6th World Congress of Nonlinear Analysts, June 25-July 1, 2012 Athens, Greece (2012) 77-87. 

• E. Tanaka and D. Krupka, On metrizability of invariant affine connections, Internat. J. Geom. Met. Mod. Phys. 9 (2012) 1250014 (15 pages), doi

2011

• J. Brajercik, Invariant variational problems on principal bundles and conservation laws, Arch. Math. (Brno), 47, No. 5 (2011) 357-366.
• J. Brajercik, Euler-Poincare reduction on frame bundles, Diff. Geom. Appl., 29 (2011) S33-S40, doi:10.1016/j.difgeo.2011.04.005. 
• D. Krupka, O. Krupkova and D. Saunders, Cartan-Lepage forms in geometric mechanics, Internat. J. of Nonlinear Mechanics 47 (2011) 1154-1160.