Scalar curvature
In Riemannian geometry, the scalar curvature (or the Ricci scalar) is the simplest curvature invariant of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the intrinsic geometry of the manifold near that point. Specifically, the scalar curvature represents the amount by which the volume of a small geodesic ball in a Riemannian manifold deviates from that of the standard ball in Euclidean space. In two dimensions, the scalar curvature is twice the Gaussian curvature, and completely characterizes the curvature of a surface. In more than two dimensions, however, the curvature of Riemannian manifolds involves more than one functionally independent quantity.
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Scalar curvature
In Riemannian geometry, the scalar curvature (or the Ricci scalar) is the simplest curvature invariant of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the intrinsic geometry of the manifold near that point. Specifically, the scalar curvature represents the amount by which the volume of a small geodesic ball in a Riemannian manifold deviates from that of the standard ball in Euclidean space. In two dimensions, the scalar curvature is twice the Gaussian curvature, and completely characterizes the curvature of a surface. In more than two dimensions, however, the curvature of Riemannian manifolds involves more than one functionally independent quantity.
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Em matemática, a curvatura esc ...... m como do tensor de curvatura.
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En geometria de Riemann, l'esc ...... ades locals podem escriure: on
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En géométrie riemannienne, la ...... conventions d'Einstein, , avec
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En matemáticas, la curvatura e ...... como del tensor de curvatura.
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In Riemannian geometry, the sc ...... ith positive scalar curvature.
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In de differentiaalmeetkunde, ...... den met een de Sitter-metriek.
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In geometria differenziale la ...... artire dal tensore di Riemann.
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Скалярна кривина (або скаляр Р ...... ора Річчі з метричним тензором
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Скалярная кривизна — один из и ...... ором.Обычно обозначается или .
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リーマン幾何学におけるスカラー曲率(すからーきょくりつ、英語 ...... )完全にリーマン幾何学の領域に特有の概念であることが分かる。
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Em matemática, a curvatura esc ...... m como do tensor de curvatura.
@pt
En geometria de Riemann, l'esc ...... una discussió més extensa). on
@ca
En géométrie riemannienne, la ...... conventions d'Einstein, , avec
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En matemáticas, la curvatura e ...... como del tensor de curvatura.
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In Riemannian geometry, the sc ...... tionally independent quantity.
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In de differentiaalmeetkunde, ...... terie is) gerelateerd aan de k
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In geometria differenziale la ...... artire dal tensore di Riemann.
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Скалярна кривина (або скаляр Р ...... ора Річчі з метричним тензором
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Скалярная кривизна — один из и ...... ором.Обычно обозначается или .
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リーマン幾何学におけるスカラー曲率(すからーきょくりつ、英語 ...... )完全にリーマン幾何学の領域に特有の概念であることが分かる。
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Courbure scalaire
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Curvatura escalar de Ricci
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Curvatura scalare
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Escalar de Ricci
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Escalar de curvatura de Ricci
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Scalaire kromming
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Scalar curvature
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Скалярна кривина
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Скалярная кривизна
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スカラー曲率
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