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In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal connection on the frame bundle – see affine connection. In the special case of a manifold isometrically embedded into a higher-dimensional Euclidean space, the covariant derivative can be viewed as the orthogonal projection of the Euclidean derivative along a tangent vector onto the manifold's tangent space. In this case the Euclidean derivative is broken into two parts, the extrinsic normal component and the intrinsic covariant derivative component.

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rdf:type
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  • Covariant derivative
  • Derivada covariante
  • Dérivée covariante
  • Derivata covariante
  • 共変微分
  • Covariante afgeleide
  • Pochodna kowariantna
  • Ковариантная производная
  • Derivada covariante
  • 共变导数
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  • La derivada covariante () es una generalización del concepto de derivada parcial () que permite extender el cálculo diferencial sobre con coordenadas cartesianas al caso de coordenadas curvilíneas en (y también al caso todavía más general de variedades diferenciables).
  • Pochodna kowariantna - tensor powstały w wyniku różniczkowania innego tensora.
  • 微分幾何学における共変微分(きょうへんびぶん、英: covariant derivative)とは、可微分多様体上の微分演算を言う。クリストッフェル並びにレヴィ=チヴィタ、リッチによって導入された。局所表示をとった場合その変換規則は共変(covariant)となる。
  • In wiskunde en natuurkunde, is de covariante afgeleide een manier om de afgeleide langs een raakvector van een variëteit te definiëren. Ruw gesproken, is het een veralgemening van de notie van afgeleide naar niet-euclidische ruimtes. In de wiskunde is het concept vooral belangrijk voor de differentiaalmeetkunde en ook in natuurkunde in de context van algemene relativiteitstheorie.
  • Ковариантная производная — обобщение понятия производной для тензорных полей на многообразиях.Понятие ковариантной производной тесно связано с понятием аффинной связности. Ковариантная производная тензорного поля в направлении касательного вектора обычно обозначается .
  • A derivada covariante () é uma generalização do conceito de derivada parcial () que permite estender o cálculo diferencial em , com coordenadas cartesianas, para o caso de coordenadas curvilíneas em (e também para o caso ainda mais geral de variedades diferenciáveis).
  • 数学上,共变导数或称协变导数是在流形上定义沿着向量场的导数的方法之一。 事实上,除了引入的风格不同之外,共变导数和联络没有实质上的区别。 在黎曼和伪黎曼流形理论中,共变导数通常指列維-奇維塔聯絡。 这里,我们给出一个向量相对于向量场的共变导数(也称为张量导数)的传统的带指标记号的简介;张量的共变导数是同一概念的推广。 本条目中,我们使用爱因斯坦记号。我们假设读者熟悉微分流形的概念特别是关于切向量的概念。
  • In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal connection on the frame bundle – see affine connection. In the special case of a manifold isometrically embedded into a higher-dimensional Euclidean space, the covariant derivative can be viewed as the orthogonal projection of the Euclidean derivative along a tangent vector onto the manifold's tangent space. In this case the Euclidean derivative is broken into two parts, the extrinsic normal component and the intrinsic covariant derivative component.
  • En géométrie différentielle, la dérivée covariante est un outil destiné à obtenir la dérivée d'un champ vectoriel sur une variété. Il n'existe pas de différence entre la dérivée covariante et la connexion, à part la manière dont elles sont introduites. Dans la théorie des variétés riemanniennes et pseudo-riemanniennes, la dérivée covariante est souvent utilisée pour la connexion de Levi-Civita.
  • In matematica, la derivata covariante estende il concetto usuale di derivata (più precisamente di derivata direzionale) presente nell'ordinario spazio euclideo ad una varietà differenziabile arbitraria. Tramite la derivata covariante è possibile calcolare la derivata di un campo vettoriale o di un più generale campo tensoriale in un punto, lungo una direzione fissata. Tramite la derivata covariante si definiscono vari tensori che misurano la curvatura della varietà. Fra questi, il tensore di Riemann ed il tensore di Ricci. Tutti questi ingredienti sono utili in relatività generale.
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