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

[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

[45] Janyška J., Geometric structures on the tangent bundle of the Einstein spacetime, preprint 2005, to apper in Arch. Math. (Brno), arXiv: math.DG/0407320.

[44] Janyška J., Modugno M., Hermitian vector fields and special phase functions, preprint 2005, arXiv: math-ph/0407320.

[43] Janyška J., Modugno M., Graded Lie algebra of Hermitian tangent valued forms, to appear in J. Math. P. Appl., arXiv: math-ph/0407320.

[42] Janyška J., Higher order Utiyama's invariant interaction, preprint 2005.

[41] Janyška J., Higher order Utiyama-like theorem, preprint 2004.

[40] Janyška J., Natural connections given by general linear and classical connections, to appear in Proc. Conf.  DGA, Prague  2004, arXiv: math.DG/0407320.

[39]  Cabras A., Janyška J., Kolář I., On the geometry of variational calculus on some functional bundles, preprint 2004, 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