Absolute Differential Calculus

Antonio Romano () and Mario Mango Furnari
Additional contact information
Antonio Romano: Università degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”
Mario Mango Furnari: Istituto di Cibernetica

Chapter Chapter 4 in The Physical and Mathematical Foundations of the Theory of Relativity, 2019, pp 103-128 from Springer

Abstract: Abstract In this chapter, we address the fundamental problem of extending the differential calculus to manifolds. This extension requires the introduction of a criterion to compare vectors belonging to different tangent spaces of the manifold. This criterion, except for some general rules that it must satisfy, is quite arbitrary. A choice of the criterion corresponds to the introduction of an affine connection on the manifold. In this chapter we define the affine connections and study their properties. On a Riemannian manifold it is possible to define only one affine connection that is compatible with the metric.

Date: 2019
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-27237-1_4

Ordering information: This item can be ordered from
http://www.springer.com/9783030272371

DOI: 10.1007/978-3-030-27237-1_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().