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Gauss–Bonnet theorem and Manifold

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Gauss–Bonnet theorem and Manifold

Gauss–Bonnet theorem vs. Manifold

The Gauss–Bonnet theorem or Gauss–Bonnet formula in differential geometry is an important statement about surfaces which connects their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic). In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

Similarities between Gauss–Bonnet theorem and Manifold

Gauss–Bonnet theorem and Manifold have 17 things in common (in Unionpedia): Angle, Atiyah–Singer index theorem, Carl Friedrich Gauss, Compact space, Curvature, Differential geometry, Digital manifold, Euler characteristic, Genus (mathematics), Geodesic, Homeomorphism, Hyperbolic geometry, Orientability, Riemannian manifold, Surface (topology), Torus, Unit disk.

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 Gauss–Bonnet theorem · Angle and Manifold · See more »

Atiyah–Singer index theorem

In differential geometry, the Atiyah–Singer index theorem, proved by, states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data).

Atiyah–Singer index theorem and Gauss–Bonnet theorem · Atiyah–Singer index theorem and Manifold · See more »

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.

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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 Gauss–Bonnet theorem · Compact space and Manifold · See more »

Curvature

In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.

Curvature and Gauss–Bonnet theorem · Curvature and Manifold · See more »

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 Gauss–Bonnet theorem · Differential geometry and Manifold · See more »

Digital manifold

In mathematics, a digital manifold is a special kind of combinatorial manifold which is defined in digital space i.e. grid cell space.

Digital manifold and Gauss–Bonnet theorem · Digital manifold and Manifold · See more »

Euler characteristic

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

Euler characteristic and Gauss–Bonnet theorem · Euler characteristic and Manifold · See more »

Genus (mathematics)

In mathematics, genus (plural genera) has a few different, but closely related, meanings.

Gauss–Bonnet theorem and Genus (mathematics) · Genus (mathematics) and Manifold · See more »

Geodesic

In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".

Gauss–Bonnet theorem and Geodesic · Geodesic and Manifold · See more »

Homeomorphism

In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.

Gauss–Bonnet theorem and Homeomorphism · Homeomorphism and Manifold · See more »

Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

Gauss–Bonnet theorem and Hyperbolic geometry · Hyperbolic geometry and Manifold · See more »

Orientability

In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.

Gauss–Bonnet theorem and Orientability · Manifold and Orientability · See more »

Riemannian manifold

In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.

Gauss–Bonnet theorem and Riemannian manifold · Manifold and Riemannian manifold · See more »

Surface (topology)

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

Gauss–Bonnet theorem and Surface (topology) · Manifold and Surface (topology) · See more »

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.

Gauss–Bonnet theorem and Torus · Manifold and Torus · See more »

Unit disk

In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1: The closed unit disk around P is the set of points whose distance from P is less than or equal to one: Unit disks are special cases of disks and unit balls; as such, they contain the interior of the unit circle and, in the case of the closed unit disk, the unit circle itself.

Gauss–Bonnet theorem and Unit disk · Manifold and Unit disk · See more »

The list above answers the following questions

Gauss–Bonnet theorem and Manifold Comparison

Gauss–Bonnet theorem has 39 relations, while Manifold has 286. As they have in common 17, the Jaccard index is 5.23% = 17 / (39 + 286).

References

This article shows the relationship between Gauss–Bonnet theorem and Manifold. To access each article from which the information was extracted, please visit:

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