Seminar

Examples of $n$-dimensional Ricci flat manifolds are Riemannian manifolds whose holonomy groups Hol(g) are subgroups of SU(n), for n=2m, and subgroups of the exceptional Lie group $G_2$, for n=7. We call them Calabi-Yau and $G_2$ manifolds, respectively. They are also examples of manifolds with special holonomy. Calibrated submanifolds of Calabi-Yau and $G_2$ manifolds are volume minimizing in their homology classes and their moduli spaces have many important applications in geometry, topology and physics. In this talk we give a report of recent research on the calibrations inside the manifolds with special holonomy.