Classification of calibrations on Rn for n 7

Abstract

In this thesis, our aim is to understand all possible calibrated submanifolds of Rn for n 7. We start with basic de nitions and tools that are used throughout this thesis. Then we study the general theory of calibrated geometries and give some interesting examples of them, following the historical development of the subject. After examining calibrations on Rn with dimensions one, two, n{u100000}1, and n{u100000}2 for arbitrary n, we focus on the nontrivial cases: classi cation of 3-dimensional calibrations on R6 and R7. On R6, we have four types of calibrations, namely special Lagrangian, Kahler, single point and double point calibrations. on R7 in addition to these four cases, we get six new types, which are called as associative, CP2, double CP1, S1, S2 and S3 calibrations.