Seminar on Geometric Complex Analysis

Seminar information archive ~03/04Next seminarFuture seminars 03/05~

Date, time & place Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Kengo Hirachi, Shigeharu Takayama


10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Hiroshi Sawai (National Institute of Technology, Numazu College)
LCK structures on compact solvmanifolds
[ Abstract ]
A locally conformal Kähler (in short LCK) manifold is said to be Vaisman if Lee form is parallel with respect to Levi-Civita connection. In this talk, we prove that a Vaisman structure on a compact solvmanifolds depends only on the form of the fundamental 2-form, and it do not depends on a complex structure. As an application, we give the structure theorem for Vaisman (completely solvable) solvmanifolds and LCK nilmanifolds. Moreover, we show the existence of LCK solvmanifolds without Vaisman structures.