Holonomy and spin geometry title introduction

Holonomy and spin geometry title introduction

1. Holonomy & Spin
Geometry
Introduction and some results

2. Holonomy Groups
Let M be a differentiable manifold.
Intuitively the holonomy of M is
obtained by studying the change
observed in tangent vectors that
are “parallel transported” around
closed paths on M.
But generally, this notion of
“Parallel Transport” has to be
given in addition by choosing a
structure called a connection.
In this way is possible to find covariant derivatives of vector fields.

3.  If g : M  T*M X T*M defines a (positive defined)
symmetric bilinear form for every point p of M, we
call it a (Riemmanian) metric
.