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- Levi-Civita_connection abstract "In Riemannian geometry, the Levi-Civita connection is a specific connection on the tangent bundle of a manifold. More specifically, it is the torsion-free metric connection, i.e., the torsion-free connection on the tangent bundle (an affine connection) preserving a given (pseudo-)Riemannian metric.The fundamental theorem of Riemannian geometry states that there is a unique connection which satisfies these properties.In the theory of Riemannian and pseudo-Riemannian manifolds the term covariant derivative is often used for the Levi-Civita connection. The components of this connection with respect to a system of local coordinates are called Christoffel symbols.The Levi-Civita connection is named after Tullio Levi-Civita, although originally "discovered" by Elwin Bruno Christoffel. Levi-Civita, along with Gregorio Ricci-Curbastro, used Christoffel's symbols to define the notion of parallel transport and explore the relationship of parallel transport with the curvature, thus developing the modern notion of holonomy.The Levi-Civita notions of intrinsic derivative and parallel displacement of a vector along a curve make sense on an abstract Riemannian manifold, even though the original motivation relied on a specific embeddingsince the definition of the Christoffel symbols make sense in any Riemannian manifold. In 1869, Christoffel discovered that the components of the intrinsic derivative of a vector transform as the components of a contravariant vector. This discovery was the real beginning of tensor analysis. It was not until 1917 that Levi-Civita interpreted the intrinsic derivative in the case of an embedded surface as the tangential component of the usual derivative in the ambient affine space.".
- Levi-Civita_connection wikiPageExternalLink Levi-CivitaConnection.html.
- Levi-Civita_connection wikiPageExternalLink LeviCivitaConnection.html.
- Levi-Civita_connection wikiPageExternalLink Levi-Civita_connection.
- Levi-Civita_connection wikiPageID "249176".
- Levi-Civita_connection wikiPageRevisionID "564755885".
- Levi-Civita_connection hasPhotoCollection Levi-Civita_connection.
- Levi-Civita_connection id "p/l058230".
- Levi-Civita_connection title "Levi-Civita connection".
- Levi-Civita_connection subject Category:Connection_(mathematics).
- Levi-Civita_connection subject Category:Riemannian_geometry.
- Levi-Civita_connection comment "In Riemannian geometry, the Levi-Civita connection is a specific connection on the tangent bundle of a manifold.".
- Levi-Civita_connection label "Conexión de Levi-Civita".
- Levi-Civita_connection label "Connessione di Levi Civita".
- Levi-Civita_connection label "Connexion de Levi-Civita".
- Levi-Civita_connection label "Levi-Civita connection".
- Levi-Civita_connection label "Levi-Civita-Zusammenhang".
- Levi-Civita_connection label "Połączenie Levi-Civita".
- Levi-Civita_connection label "Связность Леви-Чивиты".
- Levi-Civita_connection label "列维-奇维塔联络".
- Levi-Civita_connection sameAs Levi-Civita-Zusammenhang.
- Levi-Civita_connection sameAs Conexión_de_Levi-Civita.
- Levi-Civita_connection sameAs Connexion_de_Levi-Civita.
- Levi-Civita_connection sameAs Connessione_di_Levi_Civita.
- Levi-Civita_connection sameAs 레비치비타_접속.
- Levi-Civita_connection sameAs Levi-civita-verbinding.
- Levi-Civita_connection sameAs Połączenie_Levi-Civita.
- Levi-Civita_connection sameAs m.01k_nn.
- Levi-Civita_connection sameAs Q548675.
- Levi-Civita_connection sameAs Q548675.
- Levi-Civita_connection wasDerivedFrom Levi-Civita_connection?oldid=564755885.
- Levi-Civita_connection isPrimaryTopicOf Levi-Civita_connection.