(Draft) Notes on Joachim Lohkamp's Scalar Curvature Splitting:
Available soon.
This is the cumulative personal notes from studying Joachim Lohkamp's series of paper on his scalar curvature splitting theorem. As it is, the notes contain errors, since I have patchworked various documents together, some of them are written when I'm still unfamiliar with the topic. This version contains works published by Joachim Lohkamp and Matthias Kemper. An updated version is coming soon.
Master's Thesis:
Click here to access my thesis.
Abstract:
In this thesis, a review of the equality case of the positive mass theorem both in the Riemannian case and the Lorentzian case are given. In particular, a well-known compactification trick is written down in detail.
Click here to access my thesis.
Abstract:
The first part of this thesis reviews the classical results of Bochner in Riemannian geometry, proved in 1946. In the second part, the work of Lichnerowicz, in which applied a Bochner-like technique to show that compact spin manifolds of dimension n = 4k cannot admit any metrics with positive scalar curvature.
SCIE3250 – Compact Einstein Homogeneous Manifolds.