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{{DISPLAYTITLE:''p''-curvature}} ...> 0}}. It is a construction similar to a usual [[Riemann curvature tensor|curvature]], but only exists in finite characteristic. ...

[[File:Winding Number Around Point.svg|thumb|300px|This curve has total curvature 6{{pi}}, and index/turning number 3, though it only has [[winding number]] ...mmersion (mathematics)|immersed]] [[plane curve]] is the [[integral]] of [[curvature]] along a curve taken with respect to [[arc length]]: ...

...around the curve. It is a [[dimensionless quantity]] that is [[Invariant (mathematics)|invariant]] under [[Similarity (geometry)|similarity transformation]]s of If the curve is parameterized by its [[arc length]], the total absolute curvature can be expressed by the formula ...

In the [[mathematics|mathematical]] field of [[Riemannian geometry]], '''Toponogov's theorem''' ...re slowly in a region of high curvature than they would in a region of low curvature. ...

...embedded]]). There are similar examples known for every positive [[genus (mathematics)|genus]]. ...uclid.org/euclid.pjm/1102702809 | year=1986 | journal=[[Pacific Journal of Mathematics]] | volume=121 | pages=193–243 | mr = 0815044 | doi=10.2140/pjm.1986.121.19 ...

{{short description|Relates the integral of Gaussian curvature of surfaces to the Euler characteristic}} ...'', named after [[Stefan Cohn-Vossen]], relates the integral of [[Gaussian curvature]] of a non-compact [[surface (differential geometry)|surface]] to the [[Eul ...

...lding blocks other geometric objects, belonging to a well defined [[Class (mathematics)|class]]. Intuitively, it states that a [[manifold]] obtained by joining (i ...by gluing all <math>X_i</math> along all <math>C_i</math>, is also of CAT curvature <math>\leq \kappa</math>. ...

{{Short description|Theorem that curves of bounded curvature contain a unit disk}} [[File:Moon-in-puddle-green.svg|thumb|upright|A smooth simple closed curve of curvature at most one, and a unit disk enclosed by it]] ...

...of [[integral|integration]], as well as the [[integrand]], are [[Function (mathematics)|functions]] of a particular parameter. In physical applications, that para ...2010). "Hamiltonian Dynamic Equations for Fluid Films". Studies in Applied Mathematics. {{doi|10.1111/j.1467-9590.2010.00485.x}}. {{ISSN|0022-2526}}.</ref> provid ...

...lize the [[Enneper surface]] by adding handles, giving it nonzero [[Genus (mathematics)|topological genus]].<ref>{{citation|last1=Chen|first1=Chi Cheng|last2=Gack ...rst=F. J.|title=The classification of complete minimal surfaces with total curvature greater than &minus;12''π''|journal=Trans. Amer. Math. Soc.|volume=334|page ...

...metric)''' is a [[Kähler metric]] on a [[complex manifold]] whose [[scalar curvature]] is constant. A special case is a [[Kähler–Einstein metric]], and a more g Constant scalar curvature Kähler metrics are specific examples of a more general notion of canonical ...

...{{math|(''n'' + 1)}}-dimensional [[Euclidean space]] undergoes the [[mean curvature flow]], then its [[convolution]] with an appropriately scaled and time-reve | contribution = 3.1 The Monotonicity Formula for Mean Curvature Flow ...

...ose [[critical point (mathematics)|critical point]]s are [[constant scalar curvature Kähler metric]]s. The Mabuchi functional was introduced by [[Toshiki Mabuch ...analytical functional which characterises the existence of constant scalar curvature Kähler metrics. The slope at infinity of the Mabuchi functional along any [ ...

...art because the notion of "size" of the domain must also account for its [[curvature]].<ref>{{harvnb|Chavel|1984|p=77}}</ref> The theorem is due to {{harvtxt|C ...ply connected]] [[space form]] of dimension ''n'' and constant [[sectional curvature]] ''k''. Cheng's eigenvalue comparison theorem compares the first eigenvalu ...

...ed by the [[Riemann curvature tensor]], or in other words, behavior of the curvature tensor under parallel translation determines the metric. ...ttps://projecteuclid.org/euclid.ijm/1255455125|journal=Illinois Journal of Mathematics|volume=3|issue=2|pages=242–254|doi=10.1215/ijm/1255455125|issn=0019-2082|do ...

| fields = [[Mathematics]] ...s study of extremal metrics and his research on [[scalar curvature]] and Q-curvature. In CR Geometry he is known for his work on the CR embedding problem, the C ...

{{short description|Gives the Gaussian curvature of a surface from the length of a geodesic circle or its area}} ...aces]], the '''Bertrand–Diguet–Puiseux theorem''' expresses the [[Gaussian curvature]] of a surface in terms of the [[circumference]] of a [[geodesic]] circle, ...

{{about|the general mathematical concept|its optical applications|Radius of curvature (optics)}} ...le:Radius of curvature.svg|thumb|400px|Radius of curvature and [[center of curvature]]]] ...

In [[mathematics]], particularly in [[differential geometry]], an '''Osserman manifold''' is ...d by <math>R_X = R(X,\cdot)X</math>, where <math>R</math> is the [[Riemann curvature tensor]].<ref name="Nikolayevsky-2003">{{cite journal |author=Y. Nikolayevs ...

In [[mathematics]], especially [[differential topology]], the '''Gromoll–Meyer sphere''' is ...tic Sphere With Nonnegative Sectional Curvature |url= |journal=[[Annals of Mathematics]] |series=Second Series |volume=100 |issue=2 |pages=401-406 |jstor=1971078} ...