Topology, Geometry and Analysis on Surfaces

Abstract

The project Topology, geometry and analysis on surfaces discusses various topo- logical and geometric aspects of surfaces. It starts with understanding the classi- fication of closed surfaces. Then there is a brief revision of Riemannian geometry followed by discussion on the fundamental theorem of surface theory by Bon- net. After this Hilbert’s lemma and the scope of constant curvature metrics on the surfaces are briefly discussed. Thesis ends with a discussion on the Gauss- Bonnet theorem.