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Yoshihiko Matsumoto （Univ. Tokyo） |
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| Title : On the total CR Q-curvature and its variational properties |
Abstract
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Branson's Q-curvature in even-dimensional conformal geometry is a
generalization of the Gauss curvature on Riemann surfaces, whose conformal
transformation law is governed by a conformally invariant differential
operator with leading term a power of the Laplacian. I will introduce its
analog in CR geometry using the asymptotic expansion of a certain complete
Ka"hler-Einstein metric with negative curvature, or more generally an
asymptotically complex hyperbolic Einstein metric, with prescribed CR
structure at the boundary at infinity. Moreover, both in conformal and CR
geometries, the Q-curvature integrates to a global invariant that we call
the total Q-curvature. I will discuss the recent progress on its first and
second variations with emphasis in the CR case.
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Organizer: Reiko Miyaoka
Contact：
Grants-in-Aids for Scientific research：23340012 |
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