M-700 signifies the thesis work of a Ph.D. student. At present there are two students working for Ph. D. thesis under my supervision:
2) 1) The student Suha Al-Shaikh is working on the topic “Geometry of the tangent bundle of a hypersurface of a Euclidean space”. The tangent budle of a Euclidean space is Euclidean space of dimension twice that of the base Euclidean space and the differential of the immersion map of a hypersurface in a Euclidean space is the immersion of the tangent bundle in the Euclidean space (which is the tangent bundle of the base Euclidean space) this gives the induced metric on the tangent bundle of the hypersurface. This student is utilizing this idea to explore the geometry of the tangent bundle of the hypersurface.
3) 2) The student Hana Al-Sudais is working on the topic "Geometry of Ricci soliton". Ricci solitons are non-trivial solutions of the Ricci flow and they have been employed by Perelman to settle the century old Poincare' conjecture. Since then geometry of Ricci soliton is subject of interest to so many mathematicians. This student is interested in the geometry of Ricci soliton.