On the Geometry of G2 Manifolds
Date Issued
2016
Date
2016
Author(s)
Lin, Chao-Ming
Abstract
In this master thesis, we study the G2 geometry and some relevant topics. There are three main sections in this master thesis, in the first part, we state the definitions and reprove some general facts of G2 geometry, for example, if a 7-dimensional manifold is a G2 manifold, then there exists an Einstein metric on it, moreover, the metric is Ricci flat. In the second part, we summarize some volume functional on G2 manifold in date, for example, the Hitchin''s volume functional, and we analyze the stability at the critical points. In the third section, we construct an Einstein metric on certain principal bundle, technically, we give a construction of co-closed G2-structure satisfies the nearly parallel condition, hence the principal bundle contains an Einstein metric which is induced by the co-closed G2-structure.
Subjects
G2 manifold
Einstein metric
Ricci curvature
principal bundle
nearly parallel G2-structure
Type
thesis
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