Faster access than browser!Similarities between 3-manifold and Hyperbolic space
3-manifold and Hyperbolic space have 28 things in common (in Unionpedia): Ball (mathematics), Closed manifold, Compact space, Conformal map, Connected space, Constant function, Covering space, Diffeomorphism, Dimension, Elliptic geometry, Euclidean geometry, Euclidean space, Exponential growth, Fundamental group, Group action, Homogeneous space, Hyperbolic 3-manifold, Hyperbolic geometry, Mathematics, Mostow rigidity theorem, Quotient space (topology), Riemann surface, Riemannian manifold, Saddle point, Simply connected space, Sphere, Uniformization theorem, Volume form.
Ball (mathematics)
In mathematics, a ball is the space bounded by a sphere.
3-manifold and Ball (mathematics) · Ball (mathematics) and Hyperbolic space ·
Closed manifold
In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary.
3-manifold and Closed manifold · Closed manifold and Hyperbolic space ·
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).
3-manifold and Compact space · Compact space and Hyperbolic space ·
Conformal map
In mathematics, a conformal map is a function that preserves angles locally.
3-manifold and Conformal map · Conformal map and Hyperbolic space ·
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.
3-manifold and Connected space · Connected space and Hyperbolic space ·
Constant function
In mathematics, a constant function is a function whose (output) value is the same for every input value.
3-manifold and Constant function · Constant function and Hyperbolic space ·
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.
3-manifold and Covering space · Covering space and Hyperbolic space ·
Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.
3-manifold and Diffeomorphism · Diffeomorphism and Hyperbolic space ·
Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
3-manifold and Dimension · Dimension and Hyperbolic space ·
Elliptic geometry
Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.
3-manifold and Elliptic geometry · Elliptic geometry and Hyperbolic space ·
Euclidean geometry
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
3-manifold and Euclidean geometry · Euclidean geometry and Hyperbolic space ·
Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
3-manifold and Euclidean space · Euclidean space and Hyperbolic space ·
Exponential growth
Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.
3-manifold and Exponential growth · Exponential growth and Hyperbolic space ·
Fundamental group
In the mathematical field of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.
3-manifold and Fundamental group · Fundamental group and Hyperbolic space ·
Group action
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
3-manifold and Group action · Group action and Hyperbolic space ·
Homogeneous space
In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts transitively.
3-manifold and Homogeneous space · Homogeneous space and Hyperbolic space ·
Hyperbolic 3-manifold
In mathematics, more precisely in topology and differential geometry, a hyperbolic 3–manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric which has all its sectional curvatures equal to -1.
3-manifold and Hyperbolic 3-manifold · Hyperbolic 3-manifold and Hyperbolic space ·
Hyperbolic geometry
In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.
3-manifold and Hyperbolic geometry · Hyperbolic geometry and Hyperbolic space ·
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
3-manifold and Mathematics · Hyperbolic space and Mathematics ·
Mostow rigidity theorem
In mathematics, Mostow's rigidity theorem, or strong rigidity theorem, or Mostow–Prasad rigidity theorem, essentially states that the geometry of a complete, finite-volume hyperbolic manifold of dimension greater than two is determined by the fundamental group and hence unique.
3-manifold and Mostow rigidity theorem · Hyperbolic space and Mostow rigidity theorem ·
Quotient space (topology)
In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given topological space.
3-manifold and Quotient space (topology) · Hyperbolic space and Quotient space (topology) ·
Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.
3-manifold and Riemann surface · Hyperbolic space and Riemann surface ·
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.
3-manifold and Riemannian manifold · Hyperbolic space and Riemannian manifold ·
Saddle point
In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) of orthogonal function components defining the surface become zero (a stationary point) but are not a local extremum on both axes.
3-manifold and Saddle point · Hyperbolic space and Saddle point ·
Simply connected space
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.
3-manifold and Simply connected space · Hyperbolic space and Simply connected space ·
Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
3-manifold and Sphere · Hyperbolic space and Sphere ·
Uniformization theorem
In mathematics, the uniformization theorem says that every simply connected Riemann surface is conformally equivalent to one of the three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere.
3-manifold and Uniformization theorem · Hyperbolic space and Uniformization theorem ·
Volume form
In mathematics, a volume form on a differentiable manifold is a top-dimensional form (i.e., a differential form of top degree).
3-manifold and Volume form · Hyperbolic space and Volume form ·
The list above answers the following questions
- What 3-manifold and Hyperbolic space have in common
- What are the similarities between 3-manifold and Hyperbolic space
3-manifold and Hyperbolic space Comparison
3-manifold has 185 relations, while Hyperbolic space has 65. As they have in common 28, the Jaccard index is 11.20% = 28 / (185 + 65).
References
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