Sattelkörper

Sattelkörper is a term used in differential geometry and topology to describe a specific type of geometric shape or manifold. It refers to a manifold that locally resembles a saddle point, a common concept in calculus. Imagine the shape of a horse's saddle, which curves upwards in one direction and downwards in another. This characteristic curvature is what defines a sattelkörper.

More formally, a sattelkörper is a manifold with negative Gaussian curvature at certain points. Gaussian curvature is a measure of how much a surface is curved at a point. Positive curvature is found on spheres, negative curvature on saddle-shaped surfaces, and zero curvature on flat surfaces. Therefore, a sattelkörper is characterized by regions of negative curvature.

These geometric objects can arise in various contexts within mathematics. For instance, they can appear as level sets of certain functions or as solutions to differential equations. In physics, particularly in string theory and general relativity, concepts related to saddle points and negative curvature are important for understanding the structure of spacetime and the behavior of fields. The study of sattelkörper contributes to our understanding of the local and global properties of manifolds and their potential applications in different scientific disciplines.