Search for "Riemannian geometry" in article titles:

1. Riemannian geometry: Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tangent space at each point that varies smoothly from point to point). This gives, in ... (Branch of differential geometry) [100%] 2023-09-14 [Riemannian geometry]
2. Riemannian geometry: Riemmanian geometry is a non-euclidean geometric theory developed by mathematicians Bernhard Riemann and Carl Friedrich Gauss, and was later used in the Theory of Relativity. It is not as simple as euclidean geometry since it is not as close ... [100%] 2023-02-10 [Cosmology] [Mathematics]...
3. Riemannian geometry: The theory of Riemannian spaces. A Riemannian space is an -dimensional connected differentiable manifold on which a differentiable tensor field of rank 2 is given which is covariant, symmetric and positive definite. (Mathematics) [100%] 2023-10-19
4. Riemannian geometry: Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tangent space at each point that varies smoothly from point to point). This gives, in ... (Branch of differential geometry) [100%] 2024-04-02 [Riemannian geometry] [Bernhard Riemann]...
5. Riemannian geometry in the large: The branch of Riemannian geometry that examines the connections between the local and global characteristics of Riemannian manifolds. The term "Riemannian geometry in the large" usually refers to a specific range of problems and methods characteristic for geometry in the ... (Mathematics) [63%] 2023-09-23
6. Fundamental theorem of Riemannian geometry: In the mathematical field of Riemannian geometry, the fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo-Riemannian manifold) there is a unique affine connection that is torsion-free and metric-compatible, called the Levi-Civita ... (Unique existence of the Levi-Civita connection) [63%] 2023-08-01 [Articles containing proofs] [Connection (mathematics)]...
7. List of formulas in Riemannian geometry: This is a list of formulas encountered in Riemannian geometry. Einstein notation is used throughout this article. (none) [57%] 2023-06-24 [Riemannian geometry] [Mathematics-related lists]...
8. List of formulas in Riemannian geometry: This is a list of formulas encountered in Riemannian geometry. Einstein notation is used throughout this article. (none) [57%] 2024-05-09 [Riemannian geometry] [Mathematics-related lists]...
9. Pseudo-Riemannian geometry: The totality of geometric properties of surfaces and curves in a pseudo-Riemannian space $ {} ^ {l} V _ {n} $. These properties arise from the properties of a pseudo-Riemannian metric on this space, which is an indefinite quadratic form of index ... (Mathematics) [81%] 2023-10-27
10. Isometry (Riemannian geometry): In mathematics, an isometry of a manifold is any (smooth) mapping of that manifold into itself, or into another manifold that preserves the notion of distance between points. The definition of an isometry requires the notion of a metric on ... (Riemannian geometry) [81%] 2024-02-29 [Riemannian geometry]
11. Exponential map (Riemannian geometry): In Riemannian geometry, an exponential map is a map from a subset of a tangent space TpM of a Riemannian manifold (or pseudo-Riemannian manifold) M to M itself. The (pseudo) Riemannian metric determines a canonical affine connection, and the ... (Riemannian geometry) [70%] 2023-01-29 [Differential geometry] [Riemannian geometry]...
12. Exponential map (Riemannian geometry): In Riemannian geometry, an exponential map is a map from a subset of a tangent space TpM of a Riemannian manifold (or pseudo-Riemannian manifold) M to M itself. The (pseudo) Riemannian metric determines a canonical affine connection, and the ... (Riemannian geometry) [70%] 2023-09-26 [Differential geometry] [Riemannian geometry]...
13. Spectral geometry of Riemannian submersions: Let $\pi : Z \rightarrow Y$ be a Riemannian submersion. Let $D _ { Y }$ and $D _ { Z }$ be operators of Laplace type (cf. (Mathematics) [63%] 2023-10-12
14. Glossary of Riemannian and metric geometry: This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. The following articles may also be useful; they either contain specialised vocabulary or provide more detailed expositions ... (Mathematics glossary) [57%] 2023-02-20 [Differential geometry] [Glossaries of mathematics]...