On Cotangent Bundles Hamiltonian Tubes Theorem and Its Some Applications in Reduction Theory

Abdel Radi Abdel Rahman Abdel Gadir; Ragaa Mohammed Haj Ibrahim; Nedal Hassan Elbadowi Eljaneid

doi:doi:10.11648/j.ajmcm.20190402.11

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On Cotangent Bundles Hamiltonian Tubes Theorem and Its Some Applications in Reduction Theory

Abdel Radi Abdel Rahman Abdel Gadir, Ragaa Mohammed Haj Ibrahim, Nedal Hassan Elbadowi Eljaneid

Published in American Journal of Mathematical and Computer Modelling (Volume 4, Issue 2)

Received: 20 January 2019 Accepted: 25 April 2019 Published: 18 June 2019

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Abstract

This paper aims to study the Cotangent Bundles Hamiltonian Tubes theorem and its applications in reduction theory. The mathematical analysis method used. And found some results; The theory of reduction of cotangent bundles developed playing an important role in solution of the general problem for reduction a single or bit type cotangent bundles for base manifolds, possibility study of Hamiltonian tubes when the simplistic manifolds is a cotangent bundles, in the concrete case of cotangent bundles there is a strong motivation coming from geometric mechanics and geometric quantization that makes it desirable to obtain explicit fiber local models.

Published in	American Journal of Mathematical and Computer Modelling (Volume 4, Issue 2)
DOI	10.11648/j.ajmcm.20190402.11
Page(s)	31-35
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Reduction, Cotangent Bundles, Hamiltonian Tubes, Applications

References

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[3]	G. J. Rudderpost, introduction to differentiable manifolds, second edition, Springer, New York Verlag, 2012.
[4]	Hyman Bass Joseph, differential geometry and analysis on manifolds, volume 246, Springer, United States of America, 2006.
[5]	Brian. Kumar, frobenius splitting methods in geometry and representation theory, part III, progress in mathematical, 2005.
[6]	G. W. Gibbons, application of differential geometry to physics, part III, Wilber Forc Road, UK, 2006.
[7]	James J stoker, differential geometry, wily and sons New York, London, 1969.
[8]	Jeffery. M. Lee, differential geometry, analysis and physics, 2000.
[9]	John M. Lee. Introduction to smoothmanifolds, volume 218 of Graduate Texts in mathematics, Springer, New York, second edition, 2013.
[10]	Joel. W. Robbin and Ditmar Asalamon, introduction to differential geometry, third edition, university of Wisconsin, Madison, 2013.
[11]	John Opera, differential geometry and its applications, second edition, mathematical association of America eleveland state university, 2012.
[12]	Larry K Norris, symplectic geometry on tangent and cotangent bundle, North coralina state university, 2003.
[13]	M. crampin, lifting geometric object to a cotangent bundles and geometry of cotangent bundles of a tangent bundles, Walton Hall, krijgslaan, 281, Belgium.
[14]	Marian Fecko, differential geometry and lie group for physicists, third part Comenius university. Bratislava Slovakia, Cambridge, 2006.
[15]	Ph. d. thesis, cotangent bundle Hamiltonian tube theorem and its applications in reduction theory, faculty matermatiques Estaristica university polite cicada catal, 2010.
[16]	S. Akbulut. M. Ozdemir A. A. Salimov, diagonal lift in the cotangent bundles and it application Turk J. mathtubi tak, 2001.
[17]	Simonhochgerner, Singular Cotangent Bundles Reduction and spin cologero- Moser systems Wien – Vienna, 2005.
[18]	Sunil Mukhi N. Mukunda, introduction to topology, differential geometry and group theory for physicists, copyright. Wiley Eastern Limited, 1990.

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Abdel Radi Abdel Rahman Abdel Gadir, Ragaa Mohammed Haj Ibrahim, Nedal Hassan Elbadowi Eljaneid. (2019). On Cotangent Bundles Hamiltonian Tubes Theorem and Its Some Applications in Reduction Theory. American Journal of Mathematical and Computer Modelling, 4(2), 31-35. https://doi.org/10.11648/j.ajmcm.20190402.11

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ACS Style

Abdel Radi Abdel Rahman Abdel Gadir; Ragaa Mohammed Haj Ibrahim; Nedal Hassan Elbadowi Eljaneid. On Cotangent Bundles Hamiltonian Tubes Theorem and Its Some Applications in Reduction Theory. Am. J. Math. Comput. Model. 2019, 4(2), 31-35. doi: 10.11648/j.ajmcm.20190402.11

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AMA Style

Abdel Radi Abdel Rahman Abdel Gadir, Ragaa Mohammed Haj Ibrahim, Nedal Hassan Elbadowi Eljaneid. On Cotangent Bundles Hamiltonian Tubes Theorem and Its Some Applications in Reduction Theory. Am J Math Comput Model. 2019;4(2):31-35. doi: 10.11648/j.ajmcm.20190402.11

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@article{10.11648/j.ajmcm.20190402.11,
  author = {Abdel Radi Abdel Rahman Abdel Gadir and Ragaa Mohammed Haj Ibrahim and Nedal Hassan Elbadowi Eljaneid},
  title = {On Cotangent Bundles Hamiltonian Tubes Theorem and Its Some Applications in Reduction Theory},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {4},
  number = {2},
  pages = {31-35},
  doi = {10.11648/j.ajmcm.20190402.11},
  url = {https://doi.org/10.11648/j.ajmcm.20190402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20190402.11},
  abstract = {This paper aims to study the Cotangent Bundles Hamiltonian Tubes theorem and its applications in reduction theory. The mathematical analysis method used. And found some results; The theory of reduction of cotangent bundles developed playing an important role in solution of the general problem for reduction a single or bit type cotangent bundles for base manifolds, possibility study of Hamiltonian tubes when the simplistic manifolds is a cotangent bundles, in the concrete case of cotangent bundles there is a strong motivation coming from geometric mechanics and geometric quantization that makes it desirable to obtain explicit fiber local models.},
 year = {2019}
}

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TY  - JOUR
T1  - On Cotangent Bundles Hamiltonian Tubes Theorem and Its Some Applications in Reduction Theory
AU  - Abdel Radi Abdel Rahman Abdel Gadir
AU  - Ragaa Mohammed Haj Ibrahim
AU  - Nedal Hassan Elbadowi Eljaneid
Y1  - 2019/06/18
PY  - 2019
N1  - https://doi.org/10.11648/j.ajmcm.20190402.11
DO  - 10.11648/j.ajmcm.20190402.11
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 31
EP  - 35
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20190402.11
AB  - This paper aims to study the Cotangent Bundles Hamiltonian Tubes theorem and its applications in reduction theory. The mathematical analysis method used. And found some results; The theory of reduction of cotangent bundles developed playing an important role in solution of the general problem for reduction a single or bit type cotangent bundles for base manifolds, possibility study of Hamiltonian tubes when the simplistic manifolds is a cotangent bundles, in the concrete case of cotangent bundles there is a strong motivation coming from geometric mechanics and geometric quantization that makes it desirable to obtain explicit fiber local models.
VL  - 4
IS  - 2
ER  -

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Author Information

Abdel Radi Abdel Rahman Abdel Gadir

Department of Mathematics, Faculty of Education, Omdurman Islamic University, Omdurman, Sudan
Ragaa Mohammed Haj Ibrahim

Department of Mathematics, Faculty of Education, Elzaiem El Azhary University, Omdurman, Sudan
Nedal Hassan Elbadowi Eljaneid

Department of Mathematics, College of Science, Tabuk University, Tabuk, Saudi Arabia

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Plain Text BibTeX RIS

APA Style

Abdel Radi Abdel Rahman Abdel Gadir, Ragaa Mohammed Haj Ibrahim, Nedal Hassan Elbadowi Eljaneid. (2019). On Cotangent Bundles Hamiltonian Tubes Theorem and Its Some Applications in Reduction Theory. American Journal of Mathematical and Computer Modelling, 4(2), 31-35. https://doi.org/10.11648/j.ajmcm.20190402.11

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ACS Style

Abdel Radi Abdel Rahman Abdel Gadir; Ragaa Mohammed Haj Ibrahim; Nedal Hassan Elbadowi Eljaneid. On Cotangent Bundles Hamiltonian Tubes Theorem and Its Some Applications in Reduction Theory. Am. J. Math. Comput. Model. 2019, 4(2), 31-35. doi: 10.11648/j.ajmcm.20190402.11

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AMA Style

Abdel Radi Abdel Rahman Abdel Gadir, Ragaa Mohammed Haj Ibrahim, Nedal Hassan Elbadowi Eljaneid. On Cotangent Bundles Hamiltonian Tubes Theorem and Its Some Applications in Reduction Theory. Am J Math Comput Model. 2019;4(2):31-35. doi: 10.11648/j.ajmcm.20190402.11

Copy | Download

@article{10.11648/j.ajmcm.20190402.11,
  author = {Abdel Radi Abdel Rahman Abdel Gadir and Ragaa Mohammed Haj Ibrahim and Nedal Hassan Elbadowi Eljaneid},
  title = {On Cotangent Bundles Hamiltonian Tubes Theorem and Its Some Applications in Reduction Theory},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {4},
  number = {2},
  pages = {31-35},
  doi = {10.11648/j.ajmcm.20190402.11},
  url = {https://doi.org/10.11648/j.ajmcm.20190402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20190402.11},
  abstract = {This paper aims to study the Cotangent Bundles Hamiltonian Tubes theorem and its applications in reduction theory. The mathematical analysis method used. And found some results; The theory of reduction of cotangent bundles developed playing an important role in solution of the general problem for reduction a single or bit type cotangent bundles for base manifolds, possibility study of Hamiltonian tubes when the simplistic manifolds is a cotangent bundles, in the concrete case of cotangent bundles there is a strong motivation coming from geometric mechanics and geometric quantization that makes it desirable to obtain explicit fiber local models.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - On Cotangent Bundles Hamiltonian Tubes Theorem and Its Some Applications in Reduction Theory
AU  - Abdel Radi Abdel Rahman Abdel Gadir
AU  - Ragaa Mohammed Haj Ibrahim
AU  - Nedal Hassan Elbadowi Eljaneid
Y1  - 2019/06/18
PY  - 2019
N1  - https://doi.org/10.11648/j.ajmcm.20190402.11
DO  - 10.11648/j.ajmcm.20190402.11
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 31
EP  - 35
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20190402.11
AB  - This paper aims to study the Cotangent Bundles Hamiltonian Tubes theorem and its applications in reduction theory. The mathematical analysis method used. And found some results; The theory of reduction of cotangent bundles developed playing an important role in solution of the general problem for reduction a single or bit type cotangent bundles for base manifolds, possibility study of Hamiltonian tubes when the simplistic manifolds is a cotangent bundles, in the concrete case of cotangent bundles there is a strong motivation coming from geometric mechanics and geometric quantization that makes it desirable to obtain explicit fiber local models.
VL  - 4
IS  - 2
ER  -

Copy | Download