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...la''' in mathematics may refer to two different formulae in [[differential geometry]] or [[algebraic topology]]. ==Cartan formula in differential geometry== ...

...rms in Analysis, Geometry, and Physics|volume=52|series=[[Graduate Studies in Mathematics]]|first1=Ilka|last1=Agricola|author1-link= Ilka Agricola |first ...tions but have the same curvature and torsion, then they are [[congruence (geometry)|congruent]] to each other. ...

{{short description|Characterizes differential k-forms which are invariant for all Hamiltonian vector fields}} The '''Lee Hwa Chung theorem''' is a [[theorem]] in [[symplectic topology]]. ...

Several theorems are named after [[Augustin-Louis Cauchy]]. '''Cauchy theorem''' may mean: *[[Cauchy's integral theorem]] in complex analysis, also [[Cauchy's integral formula]] ...

There are several mathematical theorems named after [[Ferdinand Georg Frobenius]]. They include: * [[Frobenius theorem (differential topology)]] in differential geometry and topology for integrable subbundles ...

{{short description|Extension of the Schwarz lemma for hyperbolic geometry}} ...–Pick''' theorem is an extension of the [[Schwarz lemma]] for [[hyperbolic geometry]], such as the [[Poincaré half-plane model]]. ...

...ption|Theorem that the Clifford torus is the only minimally embedded torus in the 3-sphere}} ...journal |first=H. Blaine Jr. |last=Lawson |title=Complete minimal surfaces in S³ |journal=[[Annals of Mathematics|Ann. of Math.]] |volume=92 | ...

{{short description|Theorem in symplectic geometry which generalizes Darboux's theorem}} ...Jacobi|Jacobi]]–[[Sophus Lie|Lie]] theorem''' is a theorem in [[symplectic geometry]] which generalizes [[Darboux's theorem]]. ...

...erential geometry]] topics. See also [[glossary of differential and metric geometry]] and [[list of Lie group topics]]. ==Differential geometry of curves and surfaces== ...

In [[mathematics]], or specifically, in [[differential topology]], '''Ehresmann's lemma''' or '''Ehresmann's fibration theorem''' # a [[proper map]] (in particular, this condition is always satisfied if ''M'' is [[Compact space| ...

...fication of [[Regular curve|regular curves]] in space up to [[Translation (geometry)|translation]] and [[rotation]]. ...as a stepping stone to a larger result, rather than as a useful statement in-and-of itself. ...

{{short description|One of several theorems in different areas of mathematics}} ...ry]], '''Schur's theorem''' is a theorem of [[:de:Axel Schur|Axel Schur]]. In [[functional analysis]], '''Schur's theorem''' is often called [[Schur's pr ...

...a geometrical space invariant under the [[symmetry group]] of that space. In more recent times, the meaning has been broadened to include a view of inva ...ntegralgeometrie'', [[VEB Deutscher Verlag der Wissenschaften]]</ref> was in this connection. It follows from the [[Crofton formula|classic theorem of C ...

...wer]] minimal surface. [[Minimal surface]]s are among the objects of study in geometric analysis.]] ...differential geometry]] and [[differential topology]]. The use of [[linear differential equation|linear]] elliptic PDEs dates at least as far back as [[Hodge theor ...

{{About|the concept in geometry|the concept in [[mathematical optimization]]|Fenchel's duality theorem}} | field = [[Differential geometry]] ...

...al results factored out of proofs). See also [[list of axioms]], [[list of theorems]] and [[list of conjectures]]. {{Main category|Lemmas in algebra}} ...

...eorem]], having wide applications in nonlinear analysis and [[differential geometry]]. ...n. The directional derivative of <math>F</math> in the direction <math>v \in X</math> is defined by ...

{{Short description|In differential geometry}} ...e conjugate points.<ref>Cheeger, Ebin. ''Comparison Theorems in Riemannian Geometry''. North-Holland Publishing Company, 1975, pp. 17-18.</ref> ...

{{Short description|Branch of differential geometry}} {{General geometry |branches}} ...

In [[mathematics]], the '''Weinstein conjecture''' refers to a general existen ...Since, as is trivial to show, any orbit of a Hamiltonian flow is contained in a level set, the Weinstein conjecture is a statement about contact manifold ...