Examples of open manifolds with positive Ricci curvature and non-proper Busemann functions

Puntos clave

• To present an example of an open manifold exhibiting positive Ricci curvature alongside a non-proper Busemann function.
• Exploration of geometric properties of open manifolds
• Construction of specific manifolds to demonstrate the findings
• Analysis of the behavior of Busemann functions in the context of Ricci curvature
• Identified the first example of an open manifold with positive Ricci curvature and a non-proper Busemann function.
• Established that this example serves as a counterexample to existing theories regarding Busemann functions and Ricci curvature.