2007 Fiscal Year Final Research Report Summary
Astudy on complex and Kaehler structures on compact homogeneous manifolds
| Project/Area Number |
18540075
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Niigata University |
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Principal Investigator |
HASEGAWA Keizo Niigata University, Institute of Humanities , Social Sciences and Education, Associate Professor (00208480)
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| Co-Investigator(Kenkyū-buntansha) |
SEKIGAWA Kouei Niigata University, Institute of Sciences and Thchnology, Professor (60018661)
YOSHIHARA Hisao Niigata University, Institute of Sciences and Technology, Professor (60114807)
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| Project Period (FY) |
2006 – 2007
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| Keywords | homogeneous manifolds / complex structures / Kaehler structures |
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| Research Abstract |
In this research project, we studied one of the problems stated in "Purpose of the Project", and obtained a result "There exists a compact solvmanifold of dimension 6---actually a compact complex solvmanifold of dimension 3---which admit a continuous family of non-left-invariant complex structures as small deformations of the original complex structure". We also determine all three-dimensional compact complex-homogeneous solvmanifolds which admit pseudo-Kaehler structures. The announcement of the result has been published in "Electronic Research Announcements in Mathematical Sciences". We also published a survey article, based on the special lecture given in the annual conference of Mathematical Society of Japan, "Complex and Kaehler structures on compact homogeneous manifolds-their existence, classification and moduli problem".
As another important research activity of the project we held a workshop."Complex Geometry and Group Actions" (Niigata-shi, June 28-30, 2007); and published Proceedings of the workshop, which is available from the homepage: http://math.ed.niigata-u.ac.jp/~admin/workshop.html
We believe that this research project was successful in developing and expanding this area of research, and making it widely known to many researchers in the related fields.
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