Conformal Invariants Associated to a Measure, I: Pointwise Invariants
نویسندگان
چکیده
In this paper we study Riemannanian manifolds (M, g) equipped with a smooth measure m. In particular, we show that Riemannian invariants of (M, g) give rise to conformal densities of the Riemannian measure space (M, g,m). This leads to a natural definition of the Ricci and scalar curvatures of RM -spaces, both of which are conformally invariant. We also study some natural variational integrals.
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