2006 Fiscal Year Final Research Report Summary

Mirror symmetry conjecture over open Calabi-Yau's with boundaries

Research Project

Project/Area Number	16540077
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Geometry
Research Institution	University of Hyogo
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)
Project Period (FY)	2004 – 2006
Keywords	CR structure / isolated sing / pseudo convex
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.

(2 results)