On a New Conformal Euler-Lagrangian Equations on Para-Quaternionic Manifolds

Authors

  • Gebreel Alkhair

Abstract

In this paper we obtain Euler-Lagrange equations for quantum and classical mechanics by means of a canonical local basis {ð‘­ð‘­, ð‘®ð‘®} of V that they defined on a generalized quaternionic ð‘²ð‘²ð’‚ð’‚̈ð’‰ð’‰ð’‰ð’‰ð’‰ð’‰ð’‰ð’‰ manifold (M, g, V).

Downloads

How to Cite

On a New Conformal Euler-Lagrangian Equations on Para-Quaternionic Manifolds. (2020). Global Journal of Science Frontier Research, 20(F4), 19-32. https://www.journalofscience.org/index.php/GJSFR/article/view/2726

References

J Klein (1962) Escapes variationnals et Mecanique. 12, 1-124.

M De Leon, P Rodrigues (1989) Unknown Title. 152.

R Abraham, J Marsden, T Ratiu (2001) Manifolds, tensor analysis and applications. 483-542.

M De Leon, P Rodrigues (1987) Second-Order-Differential Equations and Non-Conservative Lagrangian Mechanics. 20, 5393-5396.

H Vries (2009) Chapter 4. Lagrangian and Hamiltonian Formalisms of the Classical Field Theory. 22, 39-60.

Mehmet Tekkoyun (2005) On para-Euler-Lagrange and para-Hamiltonian equations. 340(1-4), 7-11.

Wing Liu, Sukky Jun, Dong Qian (2005) Computational Nanomechanics of Materials. 5(5), 970-996.

M Tekkoyun, M Sari (2010) Bi-Para-mechanical systems on the bi-Lagrangian manifold. 405(10), 2390-2393.

Mehmet Tekkoyun, Yusuf Yayli (2011) MECHANICAL SYSTEMS ON GENERALIZED-QUATERNIONIC KÄHLER MANIFOLDS. 08(07), 1419-1431.

M Zambine (2006) Hamiltonian Perspective on Generalized Complex Structure. 263(3), 711-722.

M Tekkoyun (2005) On Para-Euler-Lagrange and Para-Hamiltonian Equations. 340, 7-11.

M Tekkoyun (2009) Mechanical Systems on Para-Quaternionic ̈ℎ Manifolds.

Dan Stahlke (2014) Quantum interference as a resource for quantum speedup. 90(2).

A Dancer-H, F Jorgensen -A, Swann Metric Geometries over the Split Quaternions.

L Kula, L, Y Yayli (2007) Split Quaternions and Rotations in Semi-Euclidean Space 2 4. 44, 1313-1327.

L Kula, Y Yayli (2006) Dual Split Quaternions and Serew Motion in Minkowski 3-Space Iranian. 30.

E Ata, Y Yayli (2009) Split Quaternions and Semi-Euclidean projective Spaces. 41, 1910-1915.

E Ata, Yayli (2008) A Global Condition for the Triviality of an Almost Split Quaternionic Structure on Split Complex Manifolds. 2, 1.

M Jafari, Y Yayli Generalized Quaternions and their Algebraic properties.

V Cruceanu, P Fortuny, P Gadea (1996) A Survey on Paracomplex Geometry. 26(1).

Gebreel Mohammed, Khur Baba Gebreel, M Bashir (2017) On a new dynamics on ̈ℎ manifold using local canonical basis. 4(2).

Gebreel Mohammed, Khur Baba (2017) On a New Mechanics Systems on the Standard Cliffordian ̈ℎ Manifolds Using A Canonical Local Basis. 17(4).

Gerald Folland (1970) Weyl manifolds. 4(2), 145-153.

O E Arsen'eva (1993) On the geometry of quaternion-Hermitian manifolds. 48(5), 159-160.

P Gilkey, S ľ (2010) ̈ℎ -̈ℎ curvature Wey1 manifolds.

Peter Gilkey, S Nikeevie (2011) The eta invariant for even dimensional PINc manifolds. 58(3), 243-284.

H Pedersen, Y Poon, A Swann (1993) The Einstein-Wey1 equations in complex and quaternionic geometry. 3(4), 309321.

R Miron, D Hrimiuc, H Shimada, S Sabau (2002) The geometry of Hamilton and Lagrange spaces.

H Wey (1922) Space-Time-Matter. 1.

On a New Conformal Euler-Lagrangian Equations on Para-Quaternionic  Manifolds

Published

2020-07-13

How to Cite

On a New Conformal Euler-Lagrangian Equations on Para-Quaternionic Manifolds. (2020). Global Journal of Science Frontier Research, 20(F4), 19-32. https://www.journalofscience.org/index.php/GJSFR/article/view/2726