Geometry Colloquium

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Date, time & place Friday 10:00 - 11:30 126Room #126 (Graduate School of Math. Sci. Bldg.)

2015/10/23

10:00-11:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Nobuhiko Otoba (Keio University)
Metrics of constant scalar curvature on sphere bundles (Japanese)
[ Abstract ]
This talk is based on joint work with Jimmy Petean (CIMAT).
I'd like to talk about our attempt to study the Yamabe PDE on Riemannian twisted product manifolds, more precisely, the total spaces of Riemannian submersions with totally geodesic fibers. To demonstrate how the argument works,
I construct metrics of constant scalar curvature on unit sphere bundles for real vector bundles of the type $E \oplus L$,
the Whitney sum of a vector bundle $E$ and a line bundle $L$ with respective inner products, and then estimate the number of solutions to the corresponding Yamabe PDE.