Araştırma Makalesi
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Weyl-Hamilton Equations on 3-Dimensional Normal Almost Paracontact Metric Manifold

Yıl 2020, Cilt: 4 Sayı: 2, 40 - 53, 30.12.2020

Öz

Paracontact geometry is in many ways an odd-dimensional counterpart of symplectic geometry.
Both paracontact and symplectic geometry are motivated by the mathematical formalism of classical,
analytical and dynamical mechanics. A formulation of classical mechanics is Hamiltonian mechanics.
The purpose of this paper is to study the Hamiltonian formalism for mechanical systems using
3-dimensional normal almost paracontact metric manifold.

Kaynakça

  • [1] M.M. Tripathi, E. Kilic¸ S.Y. Perktas and S. Keles¸ Indefinite Almost Paracontact Metric Manifolds, International Journal of Mathematics and Mathematical Sciences, 1-19, (2010). [2] S.Kr. Srivastava, D. Narain and K. Srivastava, Properties of ε-S Paracontact Manifold, VSRD-TNTJ, Vol. 2, (11), 559-569, (2011). [3] M. Atceken, Warped Product Semi-Invariant Submanifolds in Almost Paracontact Metric Manifolds, Mathematica Moravica, Vol. 14-1, (2010), 15-21. [4] S.S. Shukla and U.S. Verma, Paracomplex Paracontact Pseudo-Riemannian Submersions, Hindawi Publishing Corporation Geometry, 1-12, (2014). [5] Y. Gunduzalp and B. Sahin, Paracontact Semi-Riemannian Submersions, Turkish Journal of Mathematics, 37, 114-128, (2013). [6] K. Erken and C. Murathan, A Complete Study of Three-Dimensional Paracontact (κ,μ,ν)-Spaces, arxiv.org/abs/1305.1511v3, 1-26, (2013). [7] M. Manev and M. Staikova, On Almost Paracontact Riemannian Manifolds of Type (n,n), Journal of Geometry, (2001). [8] A. Bucki, Product Submanifold Almost r-Paracontact Riemannian Manifold of P-Sasakian Type, Soochov Journal of Mathematics, Volume 24, No.4, 255-259, (1998). [9] B.E. Acet, E. Kilic and S.Y. Perktas, Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection, IJMMS, 1-24, (2012). [10] M. Ahmad, A. Haseeb, J-B. Jun and S. Rahman, On Almost r-Paracontact Riemannian Manifold with a Certain Connection, Commun. Korean Math. Soc., 25, No. 2, 235-243, (2010). [11] G. Nakova and S. Zamkovoy, Almost Paracontact Manifold, arXiv:0806.3859v2, 1-17, (2009). [12] Z. Kasap and M. Tekkoyun, Mechanical Systems on Almost Para/Pseudo-Kähler--Weyl Manifolds, IJGMMP, Vol.10, No.5, (2013), 1-8. [13] G. Calvaruso and D. Perrone, Geometry of H-paracontact Metric Manifolds, arXiv:1307.7662v1, (2013). [14] S. Deshmukh and G. Khan, Almost Paracontact 3-structures on A Differentiable Manifold, Ind. J. Pure Appl. Math., 101, 442-448, (1979). [15] C. Calin, M. Crasmareanu and M. Munteanu, Slant Curves in 3-dimensional f-Kenmotsu Manifolds, J. Math. Anal. Appl., 394, (2012), 1-9. [16] G.B. Folland, Weyl Manifolds, J. Differential Geometry, 4, 145-153, (1970). [17] L. Kadosh , Topics in Weyl Geometry, Ph.D. Dissertationial, University of California, (1996). [18] M. Abreu, Kähler Geometry of Toric Manifolds In Symplectic Coordinates, arXiv:math/0004122v1, (2000), 1-24. [19] P. Gilkey, S. Nikčević and U. Simon, Geometric Realizations, Curvature Decompositions, and Weyl Manifolds. JGP, 61, (2011), 270-275. [20] H. Pedersen, Y. S. Poon, and A. Swann, The Einstein-Weyl Equations in Complex and Quaternionic Geometry, DGIA, Vol. 3, no. 4, 309-321, (1993). [21] http://en.wikipedia.org/wiki/Conformally_flat_manifold. [22] P. Gilkey and S. Nikčević, Kähler and para-Kähler curvature Weyl Manifolds, http://arxiv.org/abs/1011.4844. [23] D.J. Griffiths, Introduction to Electrodynamics. Prentice Hall. ISBN 0-13-805326-X, (1999). [24] J. Klein, Escapes Variationnels et Mécanique, Ann. Inst. Fourier, Grenoble, 12, (1962). [25] M. De Leon and P.R. Rodrigues, Methods of Differential Geometry in Analytical Mechanics, Elsevier Sc. Pub. Com. Inc., Amsterdam, (1989), 263-299. [26] B. Thidé, Electromagnetic Field Theory, (2012). [27] R.G. Martín, Electromagnetic Field Theory for Physicists and Engineers: Fundamentals and Applications, Asignatura: Electrodinámica, Físicas, Granada, (2007). [28] H. Weyl, Space-Time-Matter, Dover Publ. 1922.Translated From the 4th German Edition by H. Brose, Dover, (1952).

Weyl-Hamilton Equations on 3-Dimensional Normal Almost Paracontact Metric Manifold

Yıl 2020, Cilt: 4 Sayı: 2, 40 - 53, 30.12.2020

Öz

Paracontact geometry is in many ways an odd-dimensional counterpart of symplectic geometry.
Both paracontact and symplectic geometry are motivated by the mathematical formalism of classical,
analytical and dynamical mechanics. A formulation of classical mechanics is Hamiltonian mechanics.
The purpose of this paper is to study the Hamiltonian formalism for mechanical systems using
3-dimensional normal almost paracontact metric manifold.

Kaynakça

  • [1] M.M. Tripathi, E. Kilic¸ S.Y. Perktas and S. Keles¸ Indefinite Almost Paracontact Metric Manifolds, International Journal of Mathematics and Mathematical Sciences, 1-19, (2010). [2] S.Kr. Srivastava, D. Narain and K. Srivastava, Properties of ε-S Paracontact Manifold, VSRD-TNTJ, Vol. 2, (11), 559-569, (2011). [3] M. Atceken, Warped Product Semi-Invariant Submanifolds in Almost Paracontact Metric Manifolds, Mathematica Moravica, Vol. 14-1, (2010), 15-21. [4] S.S. Shukla and U.S. Verma, Paracomplex Paracontact Pseudo-Riemannian Submersions, Hindawi Publishing Corporation Geometry, 1-12, (2014). [5] Y. Gunduzalp and B. Sahin, Paracontact Semi-Riemannian Submersions, Turkish Journal of Mathematics, 37, 114-128, (2013). [6] K. Erken and C. Murathan, A Complete Study of Three-Dimensional Paracontact (κ,μ,ν)-Spaces, arxiv.org/abs/1305.1511v3, 1-26, (2013). [7] M. Manev and M. Staikova, On Almost Paracontact Riemannian Manifolds of Type (n,n), Journal of Geometry, (2001). [8] A. Bucki, Product Submanifold Almost r-Paracontact Riemannian Manifold of P-Sasakian Type, Soochov Journal of Mathematics, Volume 24, No.4, 255-259, (1998). [9] B.E. Acet, E. Kilic and S.Y. Perktas, Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection, IJMMS, 1-24, (2012). [10] M. Ahmad, A. Haseeb, J-B. Jun and S. Rahman, On Almost r-Paracontact Riemannian Manifold with a Certain Connection, Commun. Korean Math. Soc., 25, No. 2, 235-243, (2010). [11] G. Nakova and S. Zamkovoy, Almost Paracontact Manifold, arXiv:0806.3859v2, 1-17, (2009). [12] Z. Kasap and M. Tekkoyun, Mechanical Systems on Almost Para/Pseudo-Kähler--Weyl Manifolds, IJGMMP, Vol.10, No.5, (2013), 1-8. [13] G. Calvaruso and D. Perrone, Geometry of H-paracontact Metric Manifolds, arXiv:1307.7662v1, (2013). [14] S. Deshmukh and G. Khan, Almost Paracontact 3-structures on A Differentiable Manifold, Ind. J. Pure Appl. Math., 101, 442-448, (1979). [15] C. Calin, M. Crasmareanu and M. Munteanu, Slant Curves in 3-dimensional f-Kenmotsu Manifolds, J. Math. Anal. Appl., 394, (2012), 1-9. [16] G.B. Folland, Weyl Manifolds, J. Differential Geometry, 4, 145-153, (1970). [17] L. Kadosh , Topics in Weyl Geometry, Ph.D. Dissertationial, University of California, (1996). [18] M. Abreu, Kähler Geometry of Toric Manifolds In Symplectic Coordinates, arXiv:math/0004122v1, (2000), 1-24. [19] P. Gilkey, S. Nikčević and U. Simon, Geometric Realizations, Curvature Decompositions, and Weyl Manifolds. JGP, 61, (2011), 270-275. [20] H. Pedersen, Y. S. Poon, and A. Swann, The Einstein-Weyl Equations in Complex and Quaternionic Geometry, DGIA, Vol. 3, no. 4, 309-321, (1993). [21] http://en.wikipedia.org/wiki/Conformally_flat_manifold. [22] P. Gilkey and S. Nikčević, Kähler and para-Kähler curvature Weyl Manifolds, http://arxiv.org/abs/1011.4844. [23] D.J. Griffiths, Introduction to Electrodynamics. Prentice Hall. ISBN 0-13-805326-X, (1999). [24] J. Klein, Escapes Variationnels et Mécanique, Ann. Inst. Fourier, Grenoble, 12, (1962). [25] M. De Leon and P.R. Rodrigues, Methods of Differential Geometry in Analytical Mechanics, Elsevier Sc. Pub. Com. Inc., Amsterdam, (1989), 263-299. [26] B. Thidé, Electromagnetic Field Theory, (2012). [27] R.G. Martín, Electromagnetic Field Theory for Physicists and Engineers: Fundamentals and Applications, Asignatura: Electrodinámica, Físicas, Granada, (2007). [28] H. Weyl, Space-Time-Matter, Dover Publ. 1922.Translated From the 4th German Edition by H. Brose, Dover, (1952).
Toplam 1 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Zeki Kasap 0000-0001-8912-7734

Yayımlanma Tarihi 30 Aralık 2020
Gönderilme Tarihi 1 Haziran 2020
Kabul Tarihi 19 Ekim 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 4 Sayı: 2

Kaynak Göster

APA Kasap, Z. (2020). Weyl-Hamilton Equations on 3-Dimensional Normal Almost Paracontact Metric Manifold. Uşak Üniversitesi Fen Ve Doğa Bilimleri Dergisi, 4(2), 40-53.
AMA Kasap Z. Weyl-Hamilton Equations on 3-Dimensional Normal Almost Paracontact Metric Manifold. Uşak Üniversitesi Fen ve Doğa Bilimleri Dergisi. Aralık 2020;4(2):40-53.
Chicago Kasap, Zeki. “Weyl-Hamilton Equations on 3-Dimensional Normal Almost Paracontact Metric Manifold”. Uşak Üniversitesi Fen Ve Doğa Bilimleri Dergisi 4, sy. 2 (Aralık 2020): 40-53.
EndNote Kasap Z (01 Aralık 2020) Weyl-Hamilton Equations on 3-Dimensional Normal Almost Paracontact Metric Manifold. Uşak Üniversitesi Fen ve Doğa Bilimleri Dergisi 4 2 40–53.
IEEE Z. Kasap, “Weyl-Hamilton Equations on 3-Dimensional Normal Almost Paracontact Metric Manifold”, Uşak Üniversitesi Fen ve Doğa Bilimleri Dergisi, c. 4, sy. 2, ss. 40–53, 2020.
ISNAD Kasap, Zeki. “Weyl-Hamilton Equations on 3-Dimensional Normal Almost Paracontact Metric Manifold”. Uşak Üniversitesi Fen ve Doğa Bilimleri Dergisi 4/2 (Aralık 2020), 40-53.
JAMA Kasap Z. Weyl-Hamilton Equations on 3-Dimensional Normal Almost Paracontact Metric Manifold. Uşak Üniversitesi Fen ve Doğa Bilimleri Dergisi. 2020;4:40–53.
MLA Kasap, Zeki. “Weyl-Hamilton Equations on 3-Dimensional Normal Almost Paracontact Metric Manifold”. Uşak Üniversitesi Fen Ve Doğa Bilimleri Dergisi, c. 4, sy. 2, 2020, ss. 40-53.
Vancouver Kasap Z. Weyl-Hamilton Equations on 3-Dimensional Normal Almost Paracontact Metric Manifold. Uşak Üniversitesi Fen ve Doğa Bilimleri Dergisi. 2020;4(2):40-53.