Basic Concepts of Differential Geometry and Fibre Bundles

Mohajan, Haradhan (2015): Basic Concepts of Differential Geometry and Fibre Bundles. Published in: ABC Journal of Advanced Research , Vol. 4, No. 1 (30 March 2015): pp. 57-73.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Manifold, Fibre bundles, M bius band, Tangent space, Orientation
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling

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