Similarities between Manifold and Riemannian manifold
Manifold and Riemannian manifold have 30 things in common (in Unionpedia): Angle, Area, Atlas (topology), Bernhard Riemann, Carl Friedrich Gauss, Compact space, Connected space, Covering space, Curvature, Curve, Diffeomorphism, Differentiable manifold, Differential geometry, Divergence, Euclidean space, General relativity, Geodesic, Immersion (mathematics), Inner product space, Manifold, Nash embedding theorem, Pseudo-Riemannian manifold, Smoothness, Submanifold, Submersion (mathematics), Tangent space, Theorema Egregium, Torus, Vector field, Volume.
Angle
In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Angle and Manifold · Angle and Riemannian manifold ·
Area
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.
Area and Manifold · Area and Riemannian manifold ·
Atlas (topology)
In mathematics, particularly topology, one describes a manifold using an atlas.
Atlas (topology) and Manifold · Atlas (topology) and Riemannian manifold ·
Bernhard Riemann
Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.
Bernhard Riemann and Manifold · Bernhard Riemann and Riemannian manifold ·
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.
Carl Friedrich Gauss and Manifold · Carl Friedrich Gauss and Riemannian manifold ·
Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
Compact space and Manifold · Compact space and Riemannian manifold ·
Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.
Connected space and Manifold · Connected space and Riemannian manifold ·
Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.
Covering space and Manifold · Covering space and Riemannian manifold ·
Curvature
In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.
Curvature and Manifold · Curvature and Riemannian manifold ·
Curve
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.
Curve and Manifold · Curve and Riemannian manifold ·
Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.
Diffeomorphism and Manifold · Diffeomorphism and Riemannian manifold ·
Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
Differentiable manifold and Manifold · Differentiable manifold and Riemannian manifold ·
Differential geometry
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.
Differential geometry and Manifold · Differential geometry and Riemannian manifold ·
Divergence
In vector calculus, divergence is a vector operator that produces a scalar field, giving the quantity of a vector field's source at each point.
Divergence and Manifold · Divergence and Riemannian manifold ·
Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
Euclidean space and Manifold · Euclidean space and Riemannian manifold ·
General relativity
General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
General relativity and Manifold · General relativity and Riemannian manifold ·
Geodesic
In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".
Geodesic and Manifold · Geodesic and Riemannian manifold ·
Immersion (mathematics)
In mathematics, an immersion is a differentiable function between differentiable manifolds whose derivative is everywhere injective.
Immersion (mathematics) and Manifold · Immersion (mathematics) and Riemannian manifold ·
Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
Inner product space and Manifold · Inner product space and Riemannian manifold ·
Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
Manifold and Manifold · Manifold and Riemannian manifold ·
Nash embedding theorem
The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash, state that every Riemannian manifold can be isometrically embedded into some Euclidean space.
Manifold and Nash embedding theorem · Nash embedding theorem and Riemannian manifold ·
Pseudo-Riemannian manifold
In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.
Manifold and Pseudo-Riemannian manifold · Pseudo-Riemannian manifold and Riemannian manifold ·
Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
Manifold and Smoothness · Riemannian manifold and Smoothness ·
Submanifold
In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties.
Manifold and Submanifold · Riemannian manifold and Submanifold ·
Submersion (mathematics)
In mathematics, a submersion is a differentiable map between differentiable manifolds whose differential is everywhere surjective.
Manifold and Submersion (mathematics) · Riemannian manifold and Submersion (mathematics) ·
Tangent space
In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.
Manifold and Tangent space · Riemannian manifold and Tangent space ·
Theorema Egregium
Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a major result of differential geometry proved by Carl Friedrich Gauss that concerns the curvature of surfaces.
Manifold and Theorema Egregium · Riemannian manifold and Theorema Egregium ·
Torus
In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.
Manifold and Torus · Riemannian manifold and Torus ·
Vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.
Manifold and Vector field · Riemannian manifold and Vector field ·
Volume
Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.
The list above answers the following questions
- What Manifold and Riemannian manifold have in common
- What are the similarities between Manifold and Riemannian manifold
Manifold and Riemannian manifold Comparison
Manifold has 286 relations, while Riemannian manifold has 73. As they have in common 30, the Jaccard index is 8.36% = 30 / (286 + 73).
References
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