riemannian geometry Antonyms
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Meaning of riemannian geometry
Wordnet
riemannian geometry (n)
(mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle
riemannian geometry Sentence Examples
- Riemannian geometry provides the foundation for general relativity, which describes the curvature of spacetime.
- The intrinsic curvature of a Riemannian manifold is measured by its Riemann curvature tensor.
- Riemannian geometry enables the study of geodesics, which are the shortest paths between two points on a curved surface.
- The Levi-Civita connection is a fundamental concept in Riemannian geometry, defining the covariant derivative of vectors and tensors.
- Riemannian surfaces, which are one-dimensional Riemannian manifolds, play a crucial role in complex analysis and algebraic geometry.
- The Ricci curvature of a Riemannian manifold measures the average curvature over all directions and is used to characterize the global geometry.
- The scalar curvature of a Riemannian manifold is the trace of its Ricci curvature and provides a measure of its overall curvature.
- The theory of harmonic functions on Riemannian manifolds is closely related to Laplace's equation and has applications in physics and engineering.
- The concept of parallel transport in Riemannian geometry allows for the comparison of vectors and tensors along curves.
- Riemannian geometry is a powerful mathematical tool that has found applications in physics, engineering, and computer science.
FAQs About the word riemannian geometry
(mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle
No synonyms found.
No antonyms found.
Riemannian geometry provides the foundation for general relativity, which describes the curvature of spacetime.
The intrinsic curvature of a Riemannian manifold is measured by its Riemann curvature tensor.
Riemannian geometry enables the study of geodesics, which are the shortest paths between two points on a curved surface.
The Levi-Civita connection is a fundamental concept in Riemannian geometry, defining the covariant derivative of vectors and tensors.