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Introduction to Differentiable Manifolds

In: The Physical and Mathematical Foundations of the Theory of Relativity

Author

Listed:
  • Antonio Romano

    (Università degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”)

  • Mario Mango Furnari

    (Istituto di Cibernetica)

Abstract

In this chapter, after a brief survey of the historical development of geometry, differentiable manifolds are defined together with many geometric structures equipping them as differentiable curves and functions, tangent and cotangent spaces, differential and codifferential of a map, tangent and cotangent fiber bundles, Riemannian manifolds, and geodesics.

Suggested Citation

  • Antonio Romano & Mario Mango Furnari, 2019. "Introduction to Differentiable Manifolds," Springer Books, in: The Physical and Mathematical Foundations of the Theory of Relativity, chapter 0, pages 39-82, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-27237-1_2
    DOI: 10.1007/978-3-030-27237-1_2
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