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Seminar on Geometric Complex Analysis
Seminar information archive ～04/17｜Next seminar｜Future seminars 04/18～
| Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
2010/05/10
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshihiko MATSUMOTO (Univ. of Tokyo)
Asymptotics of ACH-Einstein metrics, and an invariant tensor of partially-integrable almost CR manifolds (JAPANESE)
Yoshihiko MATSUMOTO (Univ. of Tokyo)
Asymptotics of ACH-Einstein metrics, and an invariant tensor of partially-integrable almost CR manifolds (JAPANESE)
[ Abstract ]
To investigate strictly pseudoconvex partially-integrable almost CR manifolds as boundaries at infinity of noncompact complete Riemannian spaces, we study the Einstein equation for ACH metrics. At the jet level (of a certain order that depends only on the dimension) along the boundary, a solution uniquely exists up to the action of boundary-preserving diffeomorphisms. If we further consider higher-order solutions, without logarithmic singularities, in general we encounter an obstruction for construction, which is a local invariant tensor of the boundary. Some properties of that invariant tensor are also mentioned.
To investigate strictly pseudoconvex partially-integrable almost CR manifolds as boundaries at infinity of noncompact complete Riemannian spaces, we study the Einstein equation for ACH metrics. At the jet level (of a certain order that depends only on the dimension) along the boundary, a solution uniquely exists up to the action of boundary-preserving diffeomorphisms. If we further consider higher-order solutions, without logarithmic singularities, in general we encounter an obstruction for construction, which is a local invariant tensor of the boundary. Some properties of that invariant tensor are also mentioned.
