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Curvature tensors of singular spaces. (English) Zbl 1137.53341

Summary: A sequence of tensor-valued measures of certain singular spaces (e.g., subanalytic or convex sets) is constructed. The first three terms can be interpreted as scalar curvature, Einstein tensor and (modified) Riemann tensor. It is shown that these measures are independent of the ambient space, i.e., they are intrinsic. In contrast to this, there exists no intrinsic tensor-valued measure corresponding to the Ricci tensor.

MSC:

53C65 Integral geometry
32B20 Semi-analytic sets, subanalytic sets, and generalizations
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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