声明
摘要
第一章 Generalized Geometry Structures and Applications inPhysics
1.1 Hodge structures and linear generalized complex structures
1.1.1 Fikrations and isotropic subspaces
1.1.2 Linear generalized complex structures as Hodge structures
1.2 Generalized Κ(a)hler manifold and generalized Hodge decomposition
1.2.1 GenerMized Hodge decomposition
1.2.2 Examples
1.3 Moduli space of the(weak)generalized Calabi-Yau manifold
1.3.1 Geometry of the moduli space of SU(3,3) structures
1.3.2 Deformation and quantization of Hitchin functional
1.4 Appendix Ⅰ:the degeneration of abelian surface
1.5 AppendixⅡ:generalized geometry in flux compactification
第二章 Generalized Ricci Flow and 3D Gravity
2.1 Generalized Ricci Flow
2.2 Fixed points of generalized Ricci flow and 3D gravity
2.2.1 SL(2,R)and AdS3 gravity
2.2.2 Topological massive gravity
第三章 Hodge Theory:Nilpotent and SL2 Orbit Theorems,Mixed Hodge Structure for Hillbert Modular Surface
3.1 Nilpotent and SL2 Orbit Theorems
3.2 Hodge norm estimates
3.3 Nilpotent orbit theorem for VGPMHS
3.4 Mixed Hodge structure for Hilbert modular surface
3.4.1 Compactification for Hilbert modular surfave
3.4.2 Cohomology groups on Hilbert modular surface
3.4.3 Mixed Hodge structures on the cohomology groups valued in certain local system
参考文献
致谢
在读期间发表的学术论文与取得的研究成果