Pandit S.N. Shukla University, Shahdol (M.P) M.Sc. MATIHEMATICS SEMESTER-IV Paper V-Rlemannlan Geometry-II Syllabus
Theory Paper: Max. Marks- 42
Internal Assessment: Max. Marks- 08
Note: The question paper will consist of three sections A, B&C. Section A will consist of 7 objective ty pe questions each carrying I marks, section B will consist of 5 short answer type questions cach carry ing 3 marks and seetion C will consist of 2 long answer ty pe questions each carrying 10 marks. Section B& C will have internal choice.
Unit 1– Delinition and examples of Differentiable manifolds. Tangent spaces. Jacobian mappings.
Unit 2– Vector fields, Lie-bracket, Affine connections, Covariant derivatives, Curvature tensor, Bianchi identities.
Unit 3- Lie-derivatives, Exterior algebra and Exterior derivative.
Unit 4– Riemannian manifolds, Riemannlan connection, Curvature tensors, Sectional curvature, Schur’s theorem.
Unit 5– Geodesics in Riemannian manifolds, Projective curvature tensor, Conformal curvature tensor.
Recommended Books:
[1] R.S. Mishra, A course in Tensors with Applications to Riemannian Geometry, Pothishala Pvt. Ltd., Allahabad, 1965.
[2] B.B.Sinha, Differential Geometry-An Introduction, Shyam Prakashan Mandir, Allahabad, 1978.
Reference Books:
[1] C.E.Weatherburn, An Introduction to Tensor Calculus and Riemannian Geometry, Cambridge University Press, London , 1942 and Radha Publishing House Calcutta, Indian Edition, 1995.
[2] K.Yano, The Theory of Lie Derivatives and its Applications, North Holland Publishing Co. Amsterdam, 1957.
