Last Updated：2025/11/21
Sentence
媒介変数表示 x(u,v) を持つ曲面について、i, j, k ∈ {u, v} とすると、クリストッフェル記号 Γ^k_{ij} は二階偏導 x_ij の一階偏導 x_k 方向成分であり、曲面の曲率に関する情報を表す。
Quizzes for review
For a surface parametrized by x(u,v), and with i, j, k ∈ {u, v}, the Christoffel symbol Γk_{ij} is the component of the second derivative x_ij in the direction of the first derivative x_k, and it encodes information about the surface's curvature.
See correct answer
For a surface parametrized by x(u,v), and with i, j, k ∈ {u, v}, the Christoffel symbol Γk_{ij} is the component of the second derivative x_ij in the direction of the first derivative x_k, and it encodes information about the surface's curvature.
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Related words
Christoffel symbol
Noun
Japanese Meaning
Christoffel記号は、微分幾何学において、パラメトリゼーションされた曲面において、各点で第二微分（＝第二導函数）の成分を第一微分（＝第一導函数）の方向に射影したものとして定義され、曲面の曲率に関する情報を表す数学的対象です。
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