Connected sums of closed Riemannian manifolds and fourth order conformal invariants

Details Connected sums of closed Riemannian manifolds and fourth order conformal invariants Connected sums of closed Riemannian manifolds and fourth order conformal invariants

2008-06-24

arxiv.org/abs/0806.3800v1

Mathematics

Differential Geometry

15 pages

Scientific paper

In this note we take some initial steps in the investigation of a fourth order analogue of the Yamabe problem in conformal geometry. The Paneitz constants and the Paneitz invariants considered are believed to be very helpful to understand the topology of the underlined manifolds. We calculate how those quantities change, analogous to how the Yamabe constants and the Yamabe invariants do, under the connected sum operations.

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