2006 Fiscal Year Final Research Report Summary
Mirror symmetry conjecture over open Calabi-Yau's with boundaries
| Project/Area Number |
16540077
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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 | University of Hyogo |
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Principal Investigator |
AKAHORI Takao Univ. of Hyogo, Graduate School of Material Science, Professor, 大学院物質理学研究科, 教授 (40117560)
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| Project Period (FY) |
2004 – 2006
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| Keywords | CR structure / isolated sing / pseudo convex |
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| Research Abstract |
The purpose of this research is to study the CR geometry and apply for string theory.
Kapustin and Orlov introduce the notion A brane, which is a special type of D branes. Let W be a Kaehler manifold.
A brane consists of a submanifold of this W and line bundle with connection, which satisfies additional condition.
Inspired by the Kapustin-Orlov's work, the author constructs deformation theory of A branes, and study the relation with Hamiltonian mechanics of this submanifold. This work is still in progress and a part of my work appears in JMAA, N.322(2006), p207-p213. And especially, the new notion of CR Hamiltonian flow leads to a recent work of Einstein metric on CR manifolds.
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