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In mathematics, a '''uniformly disconnected space''' is a [[metric space]] <math>(X,d)</math> for which there exists <math>\lambda > 0</math> ...cite book| last = Heinonen| first = Juha | title = Lectures on Analysis on Metric Spaces | series = Universitext | publisher = Springer-Verlag | location = N ...

...Abstract Voronoi diagrams and their applications |book-title=Computational Geometry and its Applications |date=1988 |publisher=Springer |location=Berlin, Heide In this metric, there are two types of shortest paths. One possibility, when the two point ...

{{Short description|Type of Riemannian metric}} The '''Sasaki metric''' is a natural choice of Riemannian metric on the tangent bundle of a Riemannian manifold. ...

In [[metric geometry]], the '''Reshetnyak gluing theorem''' gives information on the structure o ...ace|complete]] [[locally compact]] [[Geodesic#Metric geometry|geodesic]] [[metric space]]s of [[CAT(k) space|CAT curvature]] <math>\leq \kappa</math>, and <m ...

In [[metric geometry]], the '''space of directions''' at a point describes the directions of cur Let (''M'', ''d'') be a [[metric space]]. First we define the '''upper angle''' for two curves starting at t ...

...an [[almost-contact manifold]] endowed with a certain kind of [[Riemannian metric]]. They are named after the Japanese mathematician Katsuei Kenmotsu. ...ta)</math> be an [[almost-contact manifold]]. One says that a [[Riemannian metric]] <math>g</math> on <math>M</math> is adapted to the almost-contact structu ...

...rman's lemma''' is a theorem used in studying [[intrinsic metric|intrinsic geometry]] of [[convex surface]]. [[Category:Differential geometry of surfaces]] ...

....svg|thumb|Example valuation function on the cube lattice which makes it a metric lattice.]] In the mathematical [[order theory|study of order]], a '''metric lattice''' {{mvar|L}} is a [[lattice (order)|lattice]] that admits a positi ...

In [[differential geometry]], the '''third fundamental form''' is a surface metric denoted by <math>\mathrm{I\!I\!I}</math>. Unlike the [[second fundamental *[[Metric tensor]] ...

...nn Weyl]]. Specifically, if <math>M</math> is a manifold with a conformal metric <math>[g]</math>, then a Weyl connection is by definition a torsion-free [[ ...e for which the symmetric part of the Ricci curvature is a multiple of the metric, by an arbitrary smooth function:<ref>{{harvnb|Mason|LeBrun|2009}}</ref> ...

{{about|the exponential map in differential geometry|discrete dynamical systems|Exponential map (discrete dynamical systems)}} In [[differential geometry]], the '''exponential map''' is a generalization of the ordinary [[exponent ...

...] of bounded length.{{r|dmpz}} The metric spaces that can be embedded into metric circles can be characterized by a four-point [[triangle inequality|triangle ...ted to and should be distinguished from a [[metric ball]], the subset of a metric space within a given radius from a central point. ...

...a certain [[metric space]] that contains all [[separable space|separable]] metric spaces in a particularly nice manner. This [[mathematics]] concept is due t ...called ''Urysohn universal''<ref>{{citation|title=Geometric embeddings of metric spaces|url=http://www.math.jyu.fi/research/reports/rep90.ps|author=Juha Hei ...

In [[mathematics]], a '''Busemann ''G''-space''' is a type of [[metric space]] first described by [[Herbert Busemann]] in 1942. If <math>(X,d)</math> is a metric space such that ...

...a smooth manifold <math>M</math> which is compatible with the [[Hermitian metric]] ...coincides with the [[Levi-Civita connection]] of the associated Riemannian metric. ...

In mathematics, the '''Besicovitch inequality''' is a [[Geometry|geometric inequality]] relating volume of a set and distances between certa ...sional cube <math>[0,1]^n</math> with a [[Riemannian geometry|Riemannian]] metric <math>g</math>. Let ...

In [[differential geometry]], the '''slice theorem''' states:<ref>{{harvnb|Audin|2004|loc=Theorem I.2. In [[algebraic geometry]], there is an analog of the slice theorem; it is called [[Luna's slice the ...

...e [[holonomy group]] of this 4-real-dimensional [[manifold]] is SU(2). The metric is generally attributed to the physicists [[Tohru Eguchi]] and [[Andrew J. ...ibed using complex coordinates <math>w_i \in \mathbb C^{d/2}</math> with a metric ...

In [[mathematics]], the '''Kuratowski embedding''' allows one to view any [[metric space]] as a subset of some [[Banach space]]. It is named after [[Kazimierz If (''X'',''d'') is a metric space, ''x''₀ is a point in ''X'', and ''C_b''(''X'') ...

...7|oclc=908865701}}</ref> The convention to call a collection of paths of a metric space bicombing is due to [[William Thurston]].<ref>{{Cite book|last=Epstei ...the map <math>\sigma_{xy}(\cdot):=\sigma(x,y,\cdot)</math> is a unit speed metric geodesic from <math>x</math> to <math>y</math>, that is, <math>\sigma_{xy}( ...