Week 06: Dual spaces; Algebra of tensors; Vector fields; Tensor fields.
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Course Material
- 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
- Chapters 18
- Department Mathematics
- Teacher
Ms. Samia Bibi
