An Introduction to Manifolds

Ovidiu Calin and Constantin Udrişte
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Ovidiu Calin: Eastern Michigan University, Department of Mathematics
Constantin Udrişte: University Politehnica of Bucharest, Faculty of Applied Sciences Department of Mathematics-Informatics

Chapter Chapter 7 in Geometric Modeling in Probability and Statistics, 2014, pp 191-222 from Springer

Abstract: Abstract This chapter contains a brief introduction to the classical theory of differential geometry. The fundamental notions presented here deal with differentiable manifolds, tangent space, vector fields, differentiable maps, 1-forms, tensors, linear connections, Riemannian manifolds, and the Levi–Civita connection. The material of this chapter forms the basis for next chapters.

Keywords: Vector Field; Riemannian Manifold; Tangent Vector; Riemannian Geometry; Ricci Tensor (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-07779-6_7

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