NEXT

• Week 01: Introduction to Tensors, Summation Convections, Dummy and free indices and Double sums.
• Week 02: First fundamental form and Second fundamental form of Vectors with examples.
• Week 03: Definition and examples of manifolds; Sub manifolds;
• Week 04: Principal curvature with roots and Gauss Weingarten's Equation
• Week 05: Tangents; Coordinate vector fields; Tangent spaces,
• Week 06: Dual spaces; Algebra of tensors; Vector fields; Tensor fields.
• Week 07: Integral curves; Affine connections and Christoffel symbols;
• Week 08: Mid Term
• Week 9: Covariant differentiation of tensor fields with examples.
• Week 10: Geodesics equations, Curve on manifold.
• Week 11: Parallel transport and its derivative.
• Week12: Lie transport, Lie derivatives and Lie Brackets.
• Week 13: Geodesic deviation and its Differential form.
• Week 14: Introduction to integration theory on manifolds.
• Week 15: Riemannian Curvature tensor
• Week 16: Ricci tensor and Ricci scalar.
• Week 17: Killing equations and Killing vector fields.
• Week 18: Final Term Exam