kódování: Central European (Win1250)
VĚDECKÁ ČINNOST
Oblastí mého vědeckého zájmu je diferenciální geometrie.
Vědecké publikace
Knižní publikace
[A] Janyška, J.; Kolář, I.; Slovák, J. (editors), Differential
Geometry and Applications, Proc. Conf. Diff. Geom. Appl., Brno
1995, Masaryk University, 1996, xiv+658 pp., ISBN 80-210-1369-9, MR ZB
847.00040
[B] Krupka D.; Janyška J., Lectures on Differential Invariants,
Folia Fac. Sci. Nat. Univ. Purkynianae Brunensis, Brno 1990, 193 pp.,
ISBN 80-210-0165-8, MR ZB 752.53004,
Research Gate.
[C] Krupka D.; Janyška (editors), Differential Geometry and Its
Applications, Proc. Conf. Diff. Geom. Appl., Brno 1989, World
Scientific, Singapore 1990, xiii+465 pp., ISBN 981-02-0188-5, MR
91b:53002, ZB 777.00040
Původní vědecké publikace
[68] Janyška J., Modugno M., Smooth and F-smooth systems, arXiv:
math.DG/2002.11983v2.
[67] Janyška J.,:
Remarks on natural differential operators with tensor fields, Archivum Mathematicum (Brno), 55(3) (2019) 289-308, DOI:10.5817/AM2019-5-289.
[66] Janyška J., Modugno M., Saller D., Infinitesimal Symmetries in Covariant Quantum Mechanics, in "Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics", Volume 2, Springer-Verlag (2018) 319-336. ISSN 2194-1009,
DOI:10.1007/978-981-13-2179-5_25.
[65] Janyška J.,
Remarks on local Lie algebras of pairs of functions, Cz. Math. Journal, 68(3) (2018) 687-709, DOI:10.21136/CMJ.2017.0626-16.
[64] Janyška J., Modugno M.,
Quantum potential in covariant quantum mechanics, Differential Geometry and its Applications, 54(2017) 175-193,
DOI:10.1016/j.difgeo.2017.03.021.
[63] Janyška J.,
On Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures, Archivum Mathematicum (Brno), 52(5) (2016) 325-339,
DOI:10.5817/AM2016-5-325.
[62] Janyška J.,
Relations between constants of motion and conserved functions, Archivum Mathematicum (Brno), 51(5) (2015) 297-313,
DOI:10.5817/AM2015-5-297.
[61] Janyška J.,
Remarks on infinitesimal symmetries of geometrical structures of the classical phase space of general relativistic test particle, International Journal of Geometrical Methods in Modern Physics, ISSN 0219-8878, 12(No. 8) (2015) 1560020,
DOI:10.1142/S0219887815600208.
[60] Janyška J.,
Hidden symmetries of the gravitational contact structure of the classical phase space of general relativistic test particle, Archivum Mathematicum (Brno), ISSN 0044-8753, 50(5) (2014) 297-316,
DOI:10.5817/AM2014-5-297.
[59] Janyška J.,
Special bracket versus Jacobi bracket on the classical phase space of general relativistic test particle, International Journal of Geometrical Methods in Modern Physics, ISSN 0219-8878, 11(NO. 7) (2014) 1460020,
DOI:10.1142/S0219887814600202.
[58] Janyška J., Vitolo R.,
On the characterization of infinitesimal symmetries of the relativistic phase space, Journal of Physics A: Mathematical and Theoretical, IOP Publishing, ISSN 1751-8113, 48 (2012) 485205,
DOI:10.1088/1751-8113/45/48/485205.
[57] Janyška J.,
Special phase functions and phase infinitesimal symmetries in classical general relativity, in AIP Conf. Proc. 1460, XX INTERNATIONAL FALL WORKSHOP ON GEOMETRY AND PHYSICS (Madrid, Spain, 2011). American Institute of Physics, 2012. ISBN 978-0-7354-1064-0, s. 135-140,
DOI:10.1063/1.4733369.
[56] Janyška J., Markl M.,
Combinatorial differential geometry and ideal
Bianchi-Ricci identitiesn II: the torsion case,
Archivum Mathematicum (Brno) 48(1) (2012) 61-80,
DOI:10.5817/AM2012-1-61.
[55] Janyška J.,
Reduction theorem for general connections,
Ann. Polonici Math. 102(3) (2011) 231-254,
DOI:10.1016/j.difgeo.2003.10.006.
[54] Janyška J.,
General covariant derivatives for general connections,
Diff. Geom. Appl. 29 suplement (2011) 116-124,
DOI:10.1016/j.difgeo.2011.04.016.
[53] Janyška J., Markl M.,
Combinatorial differential geometry and ideal
Bianchi-Ricci identities,
Adv. in Geom. 11 (2011) 509-540 ,
DOI:10.1515/advgeom.2011.017.
[52] Janyška J., Vondra J.,
Natural principal connections
on the principal gauge prolongation
of a principal bundle,
Rep. Math. Phys. 64(3) (2009) 395-415,
DOI:10.1016/S0034-4877(10)00002-9.
[51]Janyška J., Modugno M., Vitolo R., An algebraic approach to physical scales,
Acta Appl. Math. 110 (2010) 1249-1276,
DOI:10.1007/s10440-009-9505-6.
[50] Janyška J., Modugno M., Generalized geometrical structures of
odd dimensional manifolds,
J. Math. Pures Appl. 91 (2009) 211-232,
DOI:10.1016/j.matpur.2008.09.007.
[49] Janyška J., Modugno M., Geometric structures of the classical general
relativistic phase space, Inter. J. Geom. Methods
Mod. Phys. 5 (2008) 699-754,
DOI:10.1142/S021988780800303X.
[48] Janyška J., Natural and gauge-natural bundles and natural Lagrangian
structures,
in: Variations, Geometry and Physics, in honour of
D. Krupka's sixty-fifth birthday,
Nova Science Publishers 2008, 169-197.
[47] Janyška J., Utiyama's reduction method and infinitesimal symmetries of
invariant Lagrangians,
in: Symmetry and Preturbation Theory, Proc. Conf. Otranto,
World scientific 2007, 255-256,
DOI:10.1142/9789812776174_0039.
[46] Janyška J., Higher order Utiyama's invariant interaction, Rep. Math. Phys. 59 (2007) 63-81.
DOI:10.1016/S0034-4877(07)80005-X.
[45]Janyška J., Modugno M., Hermitian vector fields and special phase functions,
Inter. J. Geom. Methods
Mod. Phys. 3 (2006) 719-754,
DOI:10.1142/S0219887806001351.
[44] Janyška J., Modugno M., Quantum operators and Hermitian vector fields, in: Differential Geometry and Physics,
Proc. Conf. Tianjin,
World Scientific 2006, 256-265,
DOI:10.1142/9789812772527_0020.
[43] Janyška J., Higher order Utiyama-like theorem, Rep. Math. Phys. 58 (2006) 93-118. DOI:10.1016/S0034-4877(06)80042-X.
[42] Janyška J., Geometric structures on the tangent bundle of the
Einstein spacetime, Arch. Math. (Brno) 42 (2006) 195-203, arXiv:
math.DG/0407320.
[41] Janyška J., Modugno M., Graded Lie algebra of Hermitian tangent
valued forms, J. Math. Pures Appl. 85 (2006) 687-697,
DOI:10.1016/j.matpur.2005.11.004.
[40] Janyška J., Natural connections given by general linear and
classical connections, in: Diff. Geom. and its Appl.,
Proc. Conf., Prague 2004 (Czech Rep.), Charles University
(2005) 285-299, arXiv:
math.DG/0407320.
[39] Cabras A., Janyška J., Kolář I., On the geometry of
variational calculus on
some functional bundles, Note di Matematica 26 (2006) 51-66, arXiv:
math.DG/0407320.
[38] Janyška J., Higher order reduction
theorems for general linear connections, Note
di Matematica 23
(2004) 75-97, arXiv:
math.DG/0405488.
[37] Janyška J., Higher order reduction
theorems for classical connections, Central European Journal of
Mathematics 3
(2005) 294-308, arXiv:
math.DG/0405218.
[36] Cabras A., Janyška J., Kolář I., Functorial prolongations of
some functional bundles, Annal. Acad. Paed. Cracoviensis, Folia 23,
Studia Mathematica IV (2004) 17-30, arXiv:
math.DG/0407319.
[35] Janyška J., Reduction
theorems for general linear connections, Diff.
Geom. and its Appl. 20 (2004)
177-196.
[34] Janyška J., Modugno M., An outline of
covariant quantum mechanics, in: Proc 15th SIGRAV Conf.
Roma 2002.
[33] Janyška J., On the curvature
of tensor product connections and covariant differentials, in:
The Proceedings of the 23th Winter School Geometry and
Physics
(Srní , 2003), Supplemento ai Rendiconti del Circolo Matematico di
Palermo, Serie II, No. 72 (2004) 135-143, arXiv:
math.DG/0304042.
[32] Janyška J. and Modugno M., Covariant
pre-quantum operators, In Proceedings of the
International Conference on "Differential Geometry and Its
Applications", eds. O. Kowalski, D. Krupka and J. Slovák. Opava :
Silesian University 2002, 285-308.
[31] Janyška J. and Modugno M., Covariant
Schroedinger operator, J.
Phys. A: Math. Gen., vol. 35 (2002), no. 40, s. 8407-8434.
[30] Janyška J. and Modugno M., Uniqueness results
by covariance in covariant quantum mechanics, In Proceedings of the
Second International Symposium on "Quantum Theory and Symmetries"
(Krakow 2001), eds. E. Kapuscik, A. Horzela, New Jersey - London -
Singapore : World Scientific (2002), 404-411.
[29] Janyška J., Natural
Poisson and Jacobi structures on the tangent bundle of a
pseudo-Riemannian manifold, in: Global Differential Geometry: The
Mathematical Legacy of Alfred Gray., American
Mathematical Society (2001) Contemporary Mathematics 288, 343-347,
MR 2002j:53106.
[28] Janyška J., Modugno M. and Saller D., Covariant quantum
mechanics and quantum symmetries, In Proceedings of the
International Conference on "Recent Developments in General
Relativity",
eds. R. Cianci, R. Collina, M. Francaviglia and P. Fre.
Springer-Verlag, 2002, 285-308.
[27] Janyška J., Natural vector
fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian
manifold, Archivum
Mathematicum (Brno), 37 (2001), 143-160, MR 2002f:58004.
[26] Janyška J., A remark on
natural quantum Lagrangians and natural generalized Schroedinger
operators in Galilei quantum mechanics, Proceedings of the
Winter
School Geometry and Topology (Srní , 2000), Supplemento ai Rendiconti
del Circolo Matematico di Palermo, Serie II - No. 66 (2001), pp.
117-128, MR 2002j:81130; ZB 983.81027.
[25] Janyška J. and Modugno M., On the graded
Lie algebra of quantisable forms, Differential Geometry and
Applications, Proc. Conf. Diff. Geom.
Appl., Aug. 10 - 14, 1998, Brno, Czech republic, Masaryk University,
Brno 1999, 601-620, MR 2000i:53124; ZB 948.58001.
[24] J. Janyška, M. Modugno, On quantum vector
fields in general relativistic quantum mechanics, General
Mathematics 5 (1997), 199 - 217, Proc. of the 3rd
Internat. Workshop on Diff. Geom. and Its Appl., Sibiu - Romania 1997,
MR 2000j:81126; ZB 956.53054.
[23] Jadczyk A., Janyška J., Modugno M., Galilei general
relativistic quantum mechanics revisited, "Geometria,
Física-Matemática e outros Ensaios!, A,S. Alves, F.J. Craveiro de
Carvalho and J.A. Pereira da Silva Eds., Homenagem a António Ribeiro
Gomes, Coimbra 1998, 253-313.
[22] Janyška J., Natural Lagrangians
for quantum structures over 4-dimensionam spacetime, Rendiconti
di Matematica, Serie VII, 18, Roma (1998), 623-648, MR
2000f:53118, ZB
935.37025
[21] Janyška J. and Modugno M., Relations between
linear connections on the tangent bundle and connections on the jet
bundle of a fibred manifold, Archivum
Mathematicum (Brno), 32 (1996), 281-288, in honour of I. Kolář, MR
98c:53030; ZB 881.53015.
[20] Janyška J. and Modugno M., Quantisable functions
in general relativity, Colloque "Opérateurs differentiels
et
Physique Mathématique", Coimbra, 19-22 Juin 1995, Textos Mat. Ser. B,
24
(2000), 161-181.
[19] Janyška J. and Modugno M., Classical particle
phase space in general relativity, Differential Geometry and
Applications, Proc. Conf. Diff. Geom.
Appl., Aug. 28 - Sept. 1, 1995, Brno, Czech republic, Masaryk
University, Brno 1996, 573-602, MR 97f:53121; ZB 862.53024
[18] Janyška J., Natural symplectic
structures on the tangent bundle of a space-time, The
Proceedings of the Winter School Geometry and Topology (Srní , 1995),
Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II
-
No. 43 (1996), pp. 153-162, MR 98i:53094; ZB 908.53017
[17] Janyška J., Natural quantum
Lagrangians in Galilei quantum mechanics, Rendiconti di
Matematica, Serie VII, 15, Roma (1995), 457-468, MR 96m:81111; ZB
844.58005
[16] Janyška J., Remarks on symplectic
and contact 2-forms in relativistic theories, Bollettino U.M.I.
(7) 9-B (1994), 587-616, MR 96k:53042; ZB 960.30342
[15] Janyška J., Natural 2-forms on
the tangent bundle of a Riemannian manifold, The Proceedings of
the Winter School Geometry and Topology (Srní , 1992), Supplemento ai
Rendiconti del Circolo Matematico di Palermo, Serie II - No. 32
(1993),
pp. 165-174, MR 95g:53038; ZB 818.020
[14] Janyška J., Lie algebra
structures on $\Omega^1(M)$ and $\Omega^1(TM)$ for a Riemannian
manifold,
Rendiconti di Matematica, Serie VII, Vol. 13, Roma (1993), pp. 573-593,
MR 95d:530030; ZB 796.53034
[13] Janyška J. and Modugno M., Infinitesimal
natural and gauge-natural lifts, Differential Geometry and its
Applications 2 (1992), pp. 99-121, MR 95d:58005; ZB 780.53023
[12] Janyška J., Natural operations with projectable tangent
valued forms on a fibred manifold, Annali di Matematica Pura ed
Applicata (IV), Vol. CLIX (1991), pp. 171-187, MR 93a:58002, ZB
754.58012
[11] Janyška J., Remarks on the Nijenhuis tensor and almost
complex connections, Archivum Mathematicum (Brno), Vol. 26, No. 4
(1990) , pp. 229-240, MR 93i:53030, ZB 738.53014
[10] Janyška J., Natural and
gauge-natural operators on the space of linear connections on a vector
bundle, Diff. Geom. and Its Appl., Proc. Conf. Brno 1989, World
Scientific, Singapore 1990, pp. 58-68, MR 91g:53030, ZB 789.53015
[9] Janyška J., Connections naturally induced from the metric
tensor and its derivatives of finite order, Proc. Conf. Diff. Geom.
and Its Appl. (communications), Brno 1986, Published by J. E. Purkyně
University 1987, pp. 143-156, MR 88k:53034, ZB 653.53017
[8] Janyška J. and Kolář I., On the connections naturally
induced on the second order frame bundle, Arch. Math. (Brno)
22(1986), pp. 21-28, MR 87k:53058, ZB 628.53034
[7] Janyška J., Geometrical properties of prolongation functors,
Čas. pěst. mat., 110(1985), pp. 77-86, MR 87a:58009, ZB 582.58.002
[6] Janyška J., On natural operations with linear connections,
Czechoslovak Math. J. 35(110)1985, pp. 106-115, MR 86h:53030, ZB
594.53029
[5] Janyška J., Natural prolongations of linear connections,
Proc. Conf. Diff. Geom. and Its Appl. (Nové Město na Moravě, 1983),
Part
2, Published by J. E. Purkyně University, 1984, 129-134, MR 86k:53050,
ZB 567.53029
[4] Janyška J., On the Lie algebra of vertical prolongation
operators, Czechoslovak Math. J., 32(107) 1982, pp. 481-487, MR
84j:58012, ZB 518.58001
[3] Janyška J. and Kolář I., Lie derivatives on vector bundles,
Proc. Conf. Diff. Geom. and Its Appl. (Nové Město na Moravě, 1980),
Published by Universita Karlova, 1981, 111-116, MR 84b:58005a, ZB
494.58001
[2] Janyška J., A remark on linear functions on the sphere,
Arch. Math. 3, Scripta Fac. Sci. Nat. UJEP Brunensis, 1981,
XVII:141-150, MR 84k:52005, ZB 483.58024
[1] Janyška J., On linear functions on the sphere $S^2$,
Czechoslovak Math. J. 31(106)1981, pp. 75-82, MR 82e:53006, ZB
466.58007