riemannian manifold
Word Rarity
Very rare
Frequency: Zipf frequency 2.19 in modern English
26
Scrabble Score
18
Letters
7
Syllables
10
Unique Chars
Meaning
noun
A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product;
noun
A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product; (more formally) an ordered pair (M, g), where M is a real, smooth differentiable manifold and g its Riemannian metric.
Example Sentences
- "By definition, a Riemannian manifold M has at each point p a tangent space T#95;pM equipped with a positive-definite inner product, g#95;p; information about these inner products is encoded in the Riemannian metric tensor, g."
- "In this chapter we extend the study of eigenvalues to Riemannian manifolds whose curvature may not be constant, but is, nevertheless, bounded."
- "Further, a much harder theorem, due to J. Nash [31], says that a separable Riemannian manifold of dimension d can be isometrically embedded in #92;textstyle#92;mathbbRᴺ with N#92;le#123;#92;tfrac 1 2#125;d(d#43;1)(3d#43;11)."
- "Before we delve into the general theory of Riemannian manifolds, we pause to give it some substance by introducing a variety of "model Riemannian manifolds" that should help to motivate the general theory."
Etymology
Inflected Forms
Phrases
Frequently Paired Words
differentiable manifold
Riemannian metric
Synonyms
Riemannian space