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...iguet–Puiseux theorem''' expresses the [[Gaussian curvature]] of a surface in terms of the [[circumference]] of a [[geodesic]] circle, or the area of a g ...st=Marcel | authorlink=Marcel Berger|title= A Panoramic View of Riemannian Geometry | publisher=Springer-Verlag | year=2004 | isbn=3-540-65317-1}} ...

...least. The theorem is named for [[Leonhard Euler]] who proved the theorem in {{harv|Euler|1760}}. ..., there passes a normal plane ''P''_''X'' which cuts out a curve in ''M''. That curve has a certain [[curvature]] κ_''X'' when ...

...n invariant neighborhood of <math>G/G_x</math> (viewed as a zero section) in <math>G \times_{G_x} T_x M / T_x(G \cdot x)</math> so that it defines an [[ In [[algebraic geometry]], there is an analog of the slice theorem; it is called [[Luna's slice the ...

In mathematics, a '''Delzant polytope''' is a [[convex polytope]] in <math>\mathbb{R}^n</math> such that for each vertex <math>v</math>, exactly [[Category:Symplectic geometry]] ...

...book|url=https://books.google.com/books?id=ePf_AwAAQBAJ|title=Differential Geometry of Complex Vector Bundles|last=Kobayashi|first=Shoshichi|date=2014-07-14|pu ...first2=Shigeo|date=1954|title=Note on Kodaira-Spencer's proof of Lefschetz theorems|url=https://projecteuclid.org/euclid.pja/1195526105|journal=Proceedings of ...

...]]. The theorem was proved by the German mathematician [[Hermann Vermeil]] in 1917. ...</math>.</ref> is the only scalar invariant (or absolute invariant) linear in the second derivatives of the [[metric tensor]] <math>g_{\mu\nu}</math>. ...

...subsequently given by [[Richard Palais]] in 1957. The main difficulty lies in showing that a distance-preserving map, which is a priori only [[continuity ...row M</math> is <math display="inline">\mathcal{C}^1</math>differentiable (in both variables). This is a generalization of the easier, similar statement ...

...ntegral of [[Gaussian curvature]] of a non-compact [[surface (differential geometry)|surface]] to the [[Euler characteristic]]. It is akin to the [[Gauss–Bonn ...e Riemannian metric on the manifold. Cohn-Vossen's inequality states that in every complete Riemannian 2-manifold ''S'' with finite [[total curvature]] ...

...ng his plenary address at the [[International Congress of Mathematicians]] in [[Nice]]. Are the equators in <math>\mathbb{S}^{n+1}</math> the only smooth embedded minimal hypersurface ...

{{Short description|Algebraic geometry theorem}} In [[algebraic geometry]], the '''Reiss relation''', introduced by {{harvs|txt|last=Reiss|authorlin ...

{{Short description|Theorem in algebraic geometry}} In [[algebraic geometry]], the '''Bogomolov–Sommese vanishing theorem''' is a result related to the ...

...ll_infinity null infinity]. Let <math>\gamma</math> be a [[null geodesic]] in a [[spacetime]] <math>(M, g_{ab})</math> from a point p to null infinity, w ...th> is the Weyl tensor, and [[abstract index notation]] is used. Moreover, in the [[Petrov classification]], <math>C^{(1)}_{abcd}</math> is type N, <math ...

{{Short description|In large domains, the first Dirichlet eigenvalue of the Laplace–Beltrami opera ...ltrami operator]] is small. This general characterization is not precise, in part because the notion of "size" of the domain must also account for its [ ...

[[File:Moon-in-puddle-green.svg|thumb|upright|A smooth simple closed curve of curvature at The '''Pestov–Ionin theorem''' in the [[differential geometry]] of [[plane curve]]s states that every [[simple closed curve]] of [[curvat ...

In [[differential geometry]], a field of mathematics, the '''Lie–Palais theorem''' is a partial conver ...th>a (\alpha) = d_e \Phi (\cdot,x) (\alpha)</math> for every <math>\alpha \in \mathfrak{g}</math>. ...

...the volume of the intersection of two geodesic balls |journal=Differential Geometry and Its Applications}}</ref> It is named after [[Americans|American]] [[mat ...<math>M^n</math> is called '''pointwise Osserman''' if, for every <math>p \in M^n</math>, the [[Spectrum (functional analysis)|spectrum]] of the [[Jacobi ...

In [[differential geometry]], the '''Minkowski problem''', named after [[Hermann Minkowski]], asks for ...re ''S''^n-1 to be the surface area measure of a [[convex body]] in <math>\mathbb{R}^n</math>. Here the surface area measure ''S_K'' ...

{{Short description|Problem in differential geometry}} ...Problem (Motor Control)|its possible generalization in global differential geometry|spherical Bernstein's problem}} ...

In [[geometry]], the '''tennis ball theorem''' states that any [[smooth curve]] on the su ...Segre]], and the tennis ball theorem itself is a special case of a theorem in a 1977 paper by Joel L. Weiner.{{r|segre|global}} The name of the theorem c ...

In [[mathematics]], [[Salomon Bochner]] proved in 1946 that any [[Killing vector field]] of a compact [[Riemannian manifold]] ...length of a nonzero [[Killing vector field]] cannot have a local maximum. In particular, on a closed Riemannian manifold of negative Ricci curvature, ev ...