形状张量与嵌入流形的几何
Shape tensor and geometry of embedded manifolds
摘要：
我们回顾了嵌入流形的形状张量的概念，它有效地结合了内在和外在的几何，并允许直观地理解经典微分几何的一些基本概念，如平行运输，协变微分，曲率。我们引入形状最小化曲线，即，给定两点之间的曲线，使形状张量的积分值最小。
英文摘要：
We review the notion of shape tensor of an embedded manifold, which efficiently combines intrinsic and extrinsic geometry, and allows for intuitive understanding of some basic concepts of classical differential geometry, such as parallel transport, covariant differentiation, and curvature. We introduce shape-minimizing curves, i.e., curves between given two points that minimize integrated value of the shape tensor magnitude.
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