Basic Concepts of Differential Geometry and Fibre Bundles

  • Haradhan Kumar Mohajan Premier University
Keywords: Manifold, Fibre bundles, M bius band, Tangent space, Orientation

Abstract

The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows more complicated structures to be described and understood in terms of the relatively well-understood properties of Euclidean space. A manifold is roughly a continuous topological space which is locally similar to Euclidean space but which need not be Euclidean globally. Fibre bundle is a very interesting manifold and is formed by combining a manifold M with all its tangent spaces. A fibre bundle is a manifold that looks locally like a product of two manifolds, but is not necessarily a product globally. In this study some definitions are given to make the study easier to the common readers. An attempt has taken here to discuss elementary ideas of manifolds and fibre bundles in an easier way.

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Author Biography

Haradhan Kumar Mohajan, Premier University

Assistant Professor, Faculty of Business Studies, Premier University, Chittagong, BANGLADESH

References

Collinucci, A. and Wijns, A. (2006), Topology of Fibre bundles and Global Aspects of Gauge Theories, arXiv:hep-th/0611201v1 17 Nov 2006.

Frankel, T. (1999), The Geometry of Physics: An Introduction, Cambridge University Press, Cambridge.

Frè, P.G. (2013), Basic Concepts about Manifolds and Fibre Bundles, Gravity, a Geometric Course, Springer, Netherlands: 35–84.

Gourdin, M.L. (1982), Basics of Lie Groups, Gif Sur Yvette, France.

Hawking, S.W. and Ellis, G.F.R. (1973), The Large Scale Structure of Space-time, Cambridge University Press, Cambridge.

Joshi, P.S. (1996), Global Aspects in Gravitation and Cosmology, 2nd ed., Clarendon Press, Oxford.

Kreck, M. (2013), Orientation of Manifolds–Definition, Bulletin of the Manifold Atlas–Definition.

Lipschutz, S. (1965), General Topology, Schum’s Outline Series, McGraw-Hill Inc., Singapore.

Mohajan HK. Gravitational Collapse of a Massive Star and Black Hole Formation International Journal of Reciprocal Symmetry and Theoretical Physics. 2014;1(2):125-140.

Mohajan HK. Upper Limit of the Age of the Universe with Cosmological Constant International Journal of Reciprocal Symmetry and Theoretical Physics. 2014;1(1):43-68.

Mohajan, H.K. (2013a), Minkowski Geometry and Space-time Manifold in Relativity, Journal of Environmental Treatment Techniques, 1(2): 101–109.

Mohajan, H.K. (2013b), Singularity Theorems in General Relativity, M. Phil. Dissertation, Lambert Academic Publishing, Germany.

Nakahara, M. (1990), Geometry, Topology and Physics, Institute of Physics Publishing, London.

Nash, C. and Sen, S. (1983), Topology and Geometry for Physicists, Academic Press, San Diego.

Schutz, B.F. (1980), Geometrical Method in Mathematical Physics, Cambridge University Press, Cambridge.

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Published
2015-06-18
How to Cite
Mohajan, H. K. (2015) “Basic Concepts of Differential Geometry and Fibre Bundles”, ABC Journal of Advanced Research, 4(1), pp. 57-74. Available at: https://i-proclaim.my/journals/index.php/abcjar/article/view/44 (Accessed: 19September2019).
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