Three Anholonomy Densities According to Bishop Frame in Euclidean 3-Space
DOI:
https://doi.org/10.15407/mag15.04.510Анотація
У статті ми одержуємо три негологомні щільності за допомогою трьох перетворень репера Бішопа у тривимірному евклідовому просторі.Mathematics Subject Classification: 53Z05, 81Q70.
Ключові слова:
геометрична фаза, фаза Бішопа.Посилання
Y. Aharonov and D. Bohm, Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115 (1959), 485–490. https://doi.org/10.1017/S0022112072002307
Y. Aharonov and J. Anandan, Phase change during a cylic quantum evolution, Phys. Rev. Lett. 58 (1987), 1593–1596. https://doi.org/10.1143/JPSJ.31.293
R. Balakrishnan, Space curves, anholonomy and nonlinearity, Pramana J. Phys. 64 (2005), 607–615. https://doi.org/10.1016/0375-9601(77)90262-6
R. Balakrishnan, R. Bishop, and R. Dandoloff, Geometric phase in the classical continuous antiferromagnetic Heisenberg spin chain, Phys Rev. Lett. 64 (1990), 2107–2110. https://doi.org/10.1016/0375-9601(77)90262-6
A. Belavin and A.M. Polyakov, Metastable states of two dimensional isotropic ferromagnets, Pisma Zh. Eksp. Teor. Fiz. 22 (1975), 503–506. https://doi.org/10.1016/0893-9659(90)90138-2
M.V. Berry, Quantal phase factors accompanying adiabatic changes, Proceedings of the Royal Society of London Series A, Math. Phys. Sci. 392 (1984), 45–57. https://doi.org/10.1016/S0375-9601(01)00632-6
L.R. Bishop, There is more than one way to frame a curve, Amer. Math. Monthly 82 (1975), 246–251. https://doi.org/10.1142/S0219887810004701
M.P. Do Carmo, Differential Geometry of Curves and Surfaces. Prentice Hall, Englewood Cliffs, NJ, 1976. https://doi.org/10.1142/S0219887815500528
P. Guha, Moving space curve equations and a family of coupled KdV type systems, Chaos, Solitons and Fractals 15 (2003), 41–46. https://doi.org/10.1016/S0960-0779(02)00002-4
N. Gürbüz, Moving non-null curves according to Bishop frame in Minkowski 3-space, Int. J. Geom. Methods Mod. Phys. 12 (2015), 1550052. https://doi.org/10.1098/rspa.1984.0023
N. Gürbüz, Anholonomy according to three formulations of non-null curve evolution, Int. J. Geom. Methods Mod. Phys. 14 (2017), 1750175. https://doi.org/10.1103/PhysRevLett.58.1593
N. Gürbüz,Three class of non-lightlike curve evolution according to Darboux frame and geometric phase, Int. J. Geom. Methods Mod. Phys. 15 (2018), 1850023. https://doi.org/10.1103/PhysRev.115.485
H. Hasimoto, Motion of a vortex filament and its relation to elastica, J. Phys. Soc. Jpn. 31 (1971), 293–294. https://doi.org/10.1103/PhysRevLett.57.2471
H. Hasimoto, Soliton on a vortex filament, J. Fluid Mech. 51 (1972), 477–485. https://doi.org/10.1088/0305-4470/31/30/014
M. Lakshmanan, Continuum spin system as an exactly solvable dynamical system, Phys. Lett. A 61 (1977), 53–54. https://doi.org/10.1103/PhysRevLett.64.2107
M. Lakshmanan, Continuum spin system as an exactly solvable dynamical system, Phys. Lett. A 61 (1977), 53–54. https://doi.org/10.1142/S0219887817501754
J. Langer and R. Perline, The Hasimoto transformation and integrable flows on curves, Appl. Math. Lett. 3 (1990), 61–64. https://doi.org/10.1007/BF02706207
A. Mostafazadeh, Relativistic adiabatic approximation and geometric phase, J. Phys. A: Math. Gen. 31 (1998), 7829–7845. https://doi.org/10.1142/S0219887818500238
G. Munijara and M. Lakshmanan, Motion of space curves in three dimensional Minkowski space R13 , SO(2, 1) spin equation and defocusing nonlinear Schrödinger equation, Int. J. Geom. Methods Mod. Phys. 7 (2010) 1043–1049.
S. Murugesh and R. Balakrishnan, New connections between moving curves and soliton equations, Phys. Lett. A 290 (2001), 81–87.
A. Tomita and R.Y. Chiao, Observation of Berry’s topological phase by use of an optical fiber, Phys. Rev. Lett. 57 (1986), 937–940. https://doi.org/10.1080/00029890.1975.11993807
