This topic explores the intricate relationship between the intrinsic geometries of submanifolds and the theoretical frameworks of Grassmannian systems. It delves into how these complex geometric structures are derived from, or directly associated with, the dynamics and properties inherent in Grassmannian systems, offering crucial insights within the broader field of differential geometry.
Contact manifolds are a fascinating subject within differential geometry, often explored in the comprehensive framework of Riemannian geometry. These specific odd-dimensional smooth manifolds are equipped with a unique contact structure, which is a maximally non-integrable distribution, providing rich geometric properties. The study of contact manifolds in Riemannian geometry involves understanding the interplay between these structures and metric tensors, revealing profound insights into topology, physics, and the broader field of geometric analysis.