Real Algebraic and Analytic Geometry
Submission: 2003, December 12.
Curvature bounds which play the role of Ricci, scalar curvature and Einstein tensor bounds are introduced for subanalytic topological manifolds. It is shown, using metric properties of subanalytic sets, that an upper (lower) bound on the sectional curvature in the sense of Alexandrov implies an upper (lower) bound on the Ricci curvature and on the Einstein tensor. In the same way, an upper (lower) bound on the Ricci curvature or on the Einstein tensor implies an upper (lower) bound on the scalar curvature. .
Mathematics Subject Classification (2000): 53C23, 14P10.
Keywords and Phrases: Subanalytic sets, Alexandrov spaces, curvature bounds.
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