In the third lecture, we will continue from where we left off in the last lecture and complete the formalism of the tangent space. After this, we will extend the idea of vectors and tensors defined at a point to vector and tensor fields over the whole manifold. We will then go on to discuss a special class of tensors called differential forms, and define the wedge product and the Hodge dual. Following this, we will introduce the operations of exterior differentiation and the Lie derivative. We will then add another structure to our smooth manifold, the covariant derivative, and discuss its implications. We will see that the curvature of the space depends on the notion of covariant derivative defined on it. If time allows, we will also discuss the torsion tensor and the Riemann curvature tensor.

Details of the session:

Speaker: Simar Narula (3rd Year UG)
Date: 5th November (Wednesday)
Time: 2:00 PM
Venue: F-08A, OPB