Real Algebraic and Analytic Geometry

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85. Andreas Bernig:
Curvature tensors of singular spaces.


Submission: 2004, September 9.

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.

Mathematics Subject Classification (2000): 53C65, 32B20, 53C21.

Keywords and Phrases: Subanalytic sets, Einstein tensor, Riemann tensor.

Full text, 22p.: dvi 109k, ps.gz 216k, pdf 295k.

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