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We review the notion of shape tensor of an embedded manifold, whichefficiently combines intrinsic and extrinsic geometry, and allows for intuitiveunderstanding of some basic concepts of classical differential geometry, suchas parallel transport, covariant differentiation, and curvature. We introduceshape-minimizing curves, i.e., curves between given two points that minimizeintegrated value of the shape tensor magnitude.

Shape tensor and geometry of embedded manifolds