Některá témata diferenciání a zobecněné geometrie s aplikacemi ve fyzice.

Abstract

Differential geometry plays a prominent role in many areas of modern theoretical physics, ranging from electromagnetism and Yang-Mills to Einstein's general theory of relativity. It became a standard tool to investigate both the local and global properties of classical and quantum physical systems. Generalized geometry, as it emerged from string theory and has been first formulated mathematically by Hitchin and his students, proves to be a valuable tool for further study of quantum field theory and strings. We rigorously introduce all essential concepts of differential geometry, which are then crucial to build a basic framework of the generalized tangent bundle. 1