-
Existence results of Riemannian metrics of positive scalar curvature
You know, the ones that make us feel all warm and fuzzy inside? But before we dive into this exciting world, let’s first define…
-
Topological obstructions to Riemannian metrics with positive scalar curvature
Now, if you’re not familiar with this fancy-sounding term, let me break it down for ya: “topology” refers to how things are arranged and…
-
Riemannian Metrics and Scalar Curvature
Before anything else: Riemannian metrics. This is basically a fancy way of saying “how far apart two points are on a curvy surface.” You…
-
Riemann Curvature Tensor and Space Forms
Instead, Let’s kick this off with this topic in a more casual way! First things first: what is the Riemann curvature tensor? Well, its…
-
Gaussian Curvature and Scalar Curvature in Higher Dimensions
Instead, let me explain it like a regular person would: Imagine walking through a park on a sunny day. You see trees all around…
-
Understanding Scalar Curvature in Riemannian Geometry
It’s basically the study of curves and surfaces in space that have a metric (a fancy way of saying “measurement system”) attached to them.…
-
Ricci Decomposition in General Relativity
Instead, let me break it down for you like a true casual science communicator would do. So what is this “Ricci” thing anyway? Well,…
-
The Scalar Curvature and Its Properties
This is not your typical boring lecture where you have to take notes and pay attention. Nope, this one’s gonna be fun! Before anything…
-
The Definition and Significance of Scalar Curvature in Riemannian Geometry
So what is this mysterious “scalar curvature” thing? Well, it’s basically a way of measuring how curvy a Riemannian manifold is at each point.…
