riemannian geometry Sentence Examples

1. Riemannian geometry provides the foundation for general relativity, which describes the curvature of spacetime.
2. The intrinsic curvature of a Riemannian manifold is measured by its Riemann curvature tensor.
3. Riemannian geometry enables the study of geodesics, which are the shortest paths between two points on a curved surface.
4. The Levi-Civita connection is a fundamental concept in Riemannian geometry, defining the covariant derivative of vectors and tensors.
5. Riemannian surfaces, which are one-dimensional Riemannian manifolds, play a crucial role in complex analysis and algebraic geometry.
6. The Ricci curvature of a Riemannian manifold measures the average curvature over all directions and is used to characterize the global geometry.
7. The scalar curvature of a Riemannian manifold is the trace of its Ricci curvature and provides a measure of its overall curvature.
8. The theory of harmonic functions on Riemannian manifolds is closely related to Laplace's equation and has applications in physics and engineering.
9. The concept of parallel transport in Riemannian geometry allows for the comparison of vectors and tensors along curves.
10. Riemannian geometry is a powerful mathematical tool that has found applications in physics, engineering, and computer science.

riemannian geometry Meaning

Wordnet

riemannian geometry (n)

(mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle

Synonyms & Antonyms of riemannian geometry

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FAQs About the word riemannian geometry

What is the meaning of the word riemannian geometry

(mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle

What are the synonyms of the word riemannian geometry

No synonyms found.

What are the antonyms of the word riemannian geometry

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What is the usage of word riemannian geometry

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.

How to use the word riemannian geometry in a sentence?

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.