Explore the fascinating world of eigenvalues in Riemannian geometry with a focus on Volume 115. This resource delves into the spectral properties of Riemannian manifolds, providing insights into the relationship between geometry and analysis. Discover key concepts and applications within differential geometry and mathematical physics.
Explore the fundamental principles of Finsler and Lagrange geometries, two advanced fields within differential geometry that extend classical Riemannian concepts. This area of mathematics investigates diverse metric structures on manifolds, finding applications in theoretical physics and the calculus of variations.
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.
Explore the profound intellectual journey from Bernhard Riemann's foundational work on curved spaces to the sophisticated field of differential geometry, which provides the indispensable mathematical framework for understanding Einstein's groundbreaking theories of relativity and the very fabric of spacetime.