On Cotangent Bundles Hamiltonian Tubes Theorem and Its Some Applications in Reduction Theory
American Journal of Mathematical and Computer Modelling
Volume 4, Issue 2, June 2019, Pages: 31-35
Received: Jan. 20, 2019;
Accepted: Apr. 25, 2019;
Published: Jun. 18, 2019
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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
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.
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, American Journal of Mathematical and Computer Modelling.
Vol. 4, No. 2,
2019, pp. 31-35.
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A. A. Kirillov Lectures on the Orbit Method; volume 64, of Graduate studies in mathematics, springer. American mathematical society, printed in the USA, 2004.
Bernard. F. Schulz, geometrical method of mathematical physics, volume 296, Cambridge university press, 1980
G. J. Rudderpost, introduction to differentiable manifolds, second edition, Springer, New York Verlag, 2012.
Hyman Bass Joseph, differential geometry and analysis on manifolds, volume 246, Springer, United States of America, 2006.
Brian. Kumar, frobenius splitting methods in geometry and representation theory, part III, progress in mathematical, 2005.
G. W. Gibbons, application of differential geometry to physics, part III, Wilber Forc Road, UK, 2006.
James J stoker, differential geometry, wily and sons New York, London, 1969.
Jeffery. M. Lee, differential geometry, analysis and physics, 2000.
John M. Lee. Introduction to smoothmanifolds, volume 218 of Graduate Texts in mathematics, Springer, New York, second edition, 2013.
Joel. W. Robbin and Ditmar Asalamon, introduction to differential geometry, third edition, university of Wisconsin, Madison, 2013.
John Opera, differential geometry and its applications, second edition, mathematical association of America eleveland state university, 2012.
Larry K Norris, symplectic geometry on tangent and cotangent bundle, North coralina state university, 2003.
M. crampin, lifting geometric object to a cotangent bundles and geometry of cotangent bundles of a tangent bundles, Walton Hall, krijgslaan, 281, Belgium.
Marian Fecko, differential geometry and lie group for physicists, third part Comenius university. Bratislava Slovakia, Cambridge, 2006.
Ph. d. thesis, cotangent bundle Hamiltonian tube theorem and its applications in reduction theory, faculty matermatiques Estaristica university polite cicada catal, 2010.
S. Akbulut. M. Ozdemir A. A. Salimov, diagonal lift in the cotangent bundles and it application Turk J. mathtubi tak, 2001.
Simonhochgerner, Singular Cotangent Bundles Reduction and spin cologero- Moser systems Wien – Vienna, 2005.
Sunil Mukhi N. Mukunda, introduction to topology, differential geometry and group theory for physicists, copyright. Wiley Eastern Limited, 1990.