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Basic Concepts of Differential Geometry and Fibre Bundles

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  • Mohajan, Haradhan

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.

Suggested Citation

  • Mohajan, Haradhan, 2015. "Basic Concepts of Differential Geometry and Fibre Bundles," MPRA Paper 83002, University Library of Munich, Germany, revised 18 Feb 2015.
    • Handle: RePEc:pra:mprapa:83002
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    References listed on IDEAS

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    1. Mohajan, Haradhan, 2013. "Minkowski geometry and space-time manifold in relativity," MPRA Paper 51627, University Library of Munich, Germany, revised 03 Nov 2013.
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    Cited by:

    1. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Economic Situations of Lagrange Multiplier When Costs of Various Inputs Increase for Nonlinear Budget Constraint," MPRA Paper 116879, University Library of Munich, Germany, revised 12 Feb 2023.
    2. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Economic Aspects of Profit Maximization if Cost of Principal Raw Material Increases," MPRA Paper 117453, University Library of Munich, Germany, revised 22 Mar 2023.
    3. Mohajan, Devajit & Mohajan, Haradhan, 2023. "The Responses of an Organization for the Increase in Wage Rates: Profit Maximization Cases," MPRA Paper 118238, University Library of Munich, Germany, revised 10 Jun 2023.
    4. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Glaserian Grounded Theory and Straussian Grounded Theory: Two Standard Qualitative Research Approaches in Social Science," MPRA Paper 117017, University Library of Munich, Germany, revised 20 Feb 2023.
    5. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Broca Index: A Simple Tool to Measure Ideal Body Weight," MPRA Paper 116852, University Library of Munich, Germany, revised 18 Jan 2023.
    6. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Families of Grounded Theory: A Theoretical Structure for Novel Researchers," MPRA Paper 116752, University Library of Munich, Germany, revised 24 Jan 2023.
    7. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Economic Investigation of Lagrange Multiplier if Cost of Inputs and Budget Size of a Firm Increase: A Profit Maximization Endeavor," MPRA Paper 117993, University Library of Munich, Germany, revised 07 May 2023.
    8. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Mathematical Model for Nonlinear Budget Constraint: Economic Activities on Increased Budget," MPRA Paper 117299, University Library of Munich, Germany, revised 17 Mar 2023.
    9. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Obesity and Its Related Diseases: A New Escalating Alarming in Global Health," MPRA Paper 116797, University Library of Munich, Germany, revised 05 Feb 2023.
    10. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Long-Term Regular Exercise Increases V̇O2max for Cardiorespiratory Fitness," MPRA Paper 116962, University Library of Munich, Germany, revised 04 Feb 2023.
    11. Mohajan, Haradhan, 2016. "Global Hyperbolicity in Space-Time Manifold," MPRA Paper 83036, University Library of Munich, Germany, revised 14 Mar 2016.
    12. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Various Problems Arise in Industrial Economics If Wage Rate Increases: A Study for Nonlinear Budget Constraint," MPRA Paper 117553, University Library of Munich, Germany, revised 04 Apr 2023.
    13. Mohajan, Haradhan, 2016. "Singularities in Global Hyperbolic Space-time Manifold," MPRA Paper 82953, University Library of Munich, Germany, revised 16 Mar 2016.
    14. Mohajan, Devajit & Mohajan, Haradhan, 2023. "A Study on Nonlinear Budget Constraint of a Local Industrial Firm of Bangladesh: A Profit Maximization Investigation," MPRA Paper 117324, University Library of Munich, Germany, revised 27 Mar 2023.
    15. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis for Profit Maximization with Respect to Per Unit Cost of Subsidiary Raw Materials," MPRA Paper 116538, University Library of Munich, Germany, revised 10 Jan 2023.
    16. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis for Utility Maximization: A Study on Lagrange Multipliers and Commodity Coupons," MPRA Paper 117077, University Library of Munich, Germany, revised 06 Jan 2023.
    17. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Effects of Various Inputs for Increased Interest Rate of Capital: A Nonlinear Budget Constraint Consideration," MPRA Paper 118134, University Library of Munich, Germany, revised 06 May 2023.
    18. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis of Inputs of an Organization: A Profit Maximization Exploration," MPRA Paper 117121, University Library of Munich, Germany, revised 12 Mar 2023.
    19. Mohajan, Devajit & Mohajan, Haradhan, 2023. "An Economical Study When Cost of Irregular Raw Materials of an Industry Increases for Nonlinear Budget Constraint," MPRA Paper 118176, University Library of Munich, Germany, revised 05 May 2023.
    20. Mohajan, Devajit & Mohajan, Haradhan, 2023. "A Study on Body Fat Percentage for Physical Fitness and Prevention of Obesity: A Two Compartment Model," MPRA Paper 117158, University Library of Munich, Germany, revised Feb 2023.
    21. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Bulimia Nervosa: A Psychiatric Problem of Disorder," MPRA Paper 117258, University Library of Munich, Germany, revised 17 Mar 2023.
    22. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis between Lagrange Multipliers and Consumer Budget: Utility Maximization Case," MPRA Paper 116907, University Library of Munich, Germany, revised 19 Feb 2023.

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    More about this item

    Keywords

    Manifold; Fibre bundles; M bius band; Tangent space; Orientation;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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