Here are some suggestions for bachelor projects. Should you be interested in any of these, or have any other suggestions, you are always welcome to come and talk to me about it.
Jacobi fields, conjugate points and Jacobi's theorems.
Willmore surfaces.
Constant mean curvature surfaces.
Surfaces from integrable systems.
Minimal surfaces and Bernstein's theorem.
Complete surfaces and the theorem of Hopf-Rinow.
Riemann surfaces and the uniformization theorem.
Harmonic maps and the theorem of Ruh-Vilms.
Isothermic surfaces.
Euclidean rings, field extensions and unique factorization domains.
Field extensions and Galois theory.
Clifford algebras and spin groups.
The first fundamental group and covering spaces.
Morse theory and homology.