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Relations between intrinsic and extrinsic curvatures. (English) Zbl 1274.53024

Summary: In some sense reversing the historical development, in Section 1 it is indicated how all scalar-valued intrinsic curvatures of Riemannian manifolds can be determined in terms of the curvatures of associated Euclidean curves. This involves the consideration of arbitrary-dimensional normal sections of submanifolds in Euclidean spaces and their projections on appropriate subspaces. In terms of such normal sections of Euclidean submanifolds and of such projections, in Section 2 some comments are made concerning general inequalities for Euclidean submanifolds between their scalar curvature and their mean and normal scalar curvatures.

MSC:

53B20 Local Riemannian geometry
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