Examples of 'riemannian manifold' in a sentence
Meaning of "riemannian manifold"
riemannian manifold: In differential geometry, a Riemannian manifold is a smooth manifold equipped with a Riemannian metric, which allows for the measurement of lengths and angles. It is a fundamental concept in the study of curved spaces and is used in various mathematical and physical applications
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- 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.
- A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive definite inner product;
- an ordered pair (M, g), where M is a real, smooth differentiable manifold and g its Riemannian metric.
How to use "riemannian manifold" in a sentence
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riemannian manifold
This is a property of a two dimensional Riemannian manifold.
A closed geodesic on a Riemannian manifold is a closed curve that is also geodesic.
The data is uniformly distributed on Riemannian manifold.
The isometry group of a compact Riemannian manifold with negative Ricci curvature is discrete.
Subharmonic functions can be defined on an arbitrary Riemannian manifold.
We consider a solid body modelled by a Riemannian manifold endowed with an affine connection.
This motivates the definition of geodesic normal coordinates on a Riemannian manifold.
In a simply connected complete Riemannian manifold with nonpositive.
Sasaki metric a natural choice of Riemannian metric on the tangent bundle of Riemannian manifold.
The geodesic flow of any compact Riemannian manifold with negative sectional curvature is ergodic.
We describe how the spectrum determines a Riemannian manifold.
A smooth Riemannian manifold M is a topological space with a lot of extra structure.
The existence of such coordinates on any Riemannian manifold is established.
They state that every Riemannian manifold can be isometrically embedded in a Euclidean space Rn.
The Riemann curvature tensor directly measures the failure of this in a general Riemannian manifold.
See also
Then, we tackle the issue of Riemannian manifold learning.
On a Riemannian manifold it is an elliptic operator, while on a Lorentzian manifold it is hyperbolic.
Sormani and Wei also developed a notion called the covering spectrum of a Riemannian manifold.
In mathematics, a Riemannian manifold is said to be flat if its curvature is everywhere zero.
Such an intrinsically curved two-dimensional surface is a simple example of a Riemannian manifold.
In mathematics, a sub-Riemannian manifold is a certain type of generalization of a Riemannian manifold.
Abstract, In this thesis, we study the medians of a probability measure in a Riemannian manifold.
This is a generalization of a Riemannian manifold in which the requirement of positive-definiteness is relaxed.
However, the Ricci curvature has no analogous topological interpretation on a generic Riemannian manifold.
Put differently, a Riemannian manifold is a space constructed by deforming and patching together Euclidean spaces.
This gives a three-dimensional smooth manifold which becomes a Riemannian manifold when we add the metric structure.
Let (M, g) be a Riemannian manifold or pseudo-Riemannian manifold.
The Riemann sphere is only a conformal manifold, not a Riemannian manifold.
With this definition of distance, geodesics in a Riemannian manifold are then the locally distance-minimizing paths.
In the third chapter, we study the MTW tensor on compact Riemannian manifold.
Let ( M, g ) be a compact m-dimensional Riemannian manifold with injectivity radius injM.
Statement of the theorem = = Suppose formula 1 is a compact two-dimensional Riemannian manifold with boundary formula 2.
Diameter = = = The diameter of a Riemannian manifold " M " is defined by:formula 33The diameter is invariant under global isometries.
In differential geometry, a G2 manifold is a seven-dimensional Riemannian manifold with holonomy group contained in G2.
Every compact, simply connected, conformally Euclidean Riemannian manifold is conformally equivalent to the round sphere.
In Chapter 1, 2 and 4, we study Riesz transforms on Riemannian manifold and on graphs.
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Manifold pressure should be checked with a manometer
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Examples of using Riemannian
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Phenomenon of bifurcation in yamabe problem on riemannian manifolds with boundary
A singular riemannian foliation in m is a singular foliation with locally equidistant leaves
The purpose of this thesis is to study singular elliptic problems in riemannian manifolds
