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Lanjutan Satu Kaitan Koszul Mendatar Berbentuk Maurer-Cartan

Tahir Ahmad, (2005) Lanjutan Satu Kaitan Koszul Mendatar Berbentuk Maurer-Cartan. Bulletin of the Malaysian Mathematical Sciences Society, 28 (2). pp. 191-204. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v28n2/v28n2p10.pdf

Affiliations

Universiti Teknologi Malaysia, Fakulti Sains, Jabatan Matematik

Abstract

In this paper a formulation of a connection for tangent bundle of a unit sphere; $T(S^{2})$ is presented. The connection is developed using properties of tangent bundle for $S^2$ and Lie differential operator. The connection is presented by a theorem and is found to be a flat Koszul connection. The connection is then generalized to any vector bundles $(E,q,B)$ followed by several theorems which described its properties. Finally the extension of the developed connection turns to be a Maurer-Cartan form.


2000 Mathematics Subject Classification: 53C07

Item Type:Journal
Keywords:Manifold, berkas vektor, operator terbitan Lie, pemetaan kovarian, kaitan mendatar, bentuk Maurer-Cartan
Subjects:Q Science, Computer Science
ID Code:1423

[1] T. Ahmad, Vektor berkas trirangkap, Pros. Simp. Keb. Sains Matematik ke-7, Shah Alam, Selangor, 3-5 Dis. 1996, 319—325.

[2] K. Konieczna and P. Urbanski, Double vector bundles and duality, Arch. Math. (Brno) 35(1) (1999), 59—95.

[3] B. O’Neill, Elementary Differential Geometry, Academic Press, New York, 1966.

[4] T. Ahmad, Satu kaitan Koszul mendatar untuk berkas tangen unit sfera (TS²,\pi,S²), Matematika 16(1) (2000), 41—46.

[5] T. Ahmad, Pengitlakan satu kaitan Koszul mendatar (TS²,\pi,S²) kepada (E,q,B), Matematika 16(2) (2000), 95—100.

[6] R. Abraham and J. E. Marsden, Foundations of Mechanics, Second edition, Benjamin/Cummings, Reading, Mass., 1985.

[7] G. Lugo, Notes On Differential Geometry in Physics, Department of Mathematical Sciences, Univ. North Carolina, March 1998, 1—56.

[8] T. Ahmad, Permukaan Riemann: S², Matematika 19(1) (1993), 9—17.

[9] F. E. Burstall, Harmonic tori in Lie groups, in Geometry and topology of submanifolds, III (Leeds, 1990), 73—80, World Sci. Publishing, River Edge, NJ.

[10] P. J. Olver and J. Pohjanpelto, Moving Frames for Pseudo-Groups. I. The Maurer-Cartan Forms, School of Mathematics, University of Minnesota, Minneapolis, MN 55455, October 13, 2003, 1—25.

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