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...efer to two different formulae in [[differential geometry]] or [[algebraic topology]]. ==Cartan formula in differential geometry== ...

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

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

...y)|twisting]], crumpling and bending, but not tearing or [[Quotient space (topology)|gluing]]. ...line (geometry)|line]] and a [[surface (mathematics)|surface]]; [[compact (topology)|compactness]], which allows distinguishing between a line and a circle; [[ ...

...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 | ...

* [[Abelian group]], a group in which the binary operation is commutative ===Topology and number theory=== ...

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

{{short description|On immersions of smooth m-dimensional manifolds in 2m-space and (2m-1) space}} ...imilarly, every smooth <math>m</math>-dimensional manifold can be immersed in the <math>2m-1</math>-dimensional sphere (this removes the <math>m>1</math> ...

==Theorems of which articles are primarily devoted to proving them== ==Articles devoted to theorems of which a (sketch of a) proof is given== ...

...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 ...

...f index theorem''') is an important theorem that is used in [[differential topology]]. It is named after [[Henri Poincaré]] and [[Heinz Hopf]]. ...centres and one saddle or one centre, but never just the saddle. (Here for in case of a [[Hamiltonian system]])]] ...

{{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 ...

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

{{Short description|Theorem in mathematical analysis}} ...has [[Lebesgue measure]] 0. This makes the set of critical values "small" in the sense of a [[generic property]]. The theorem is named for [[Anthony Mor ...

...e function theorem]], 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|Theorems generalizing the Brouwer fixed-point theorem}} ...cations, for example, to the proof of [[existence theorem]]s for [[partial differential equation]]s. ...

...d. If ''M'' is already a topological manifold, it is required that the new topology be identical to the existing one. ...tial structures</ref> is defined using a '''''C''^''k''-[[atlas (topology)|atlas]]''', which is a set of [[bijections]] called '''charts''' between s ...

...[Raoul Bott|Bott, R.]] and Tu, L.W., 1982. Differential forms in algebraic topology (Vol. 82, pp. xiv+-331). New York: Springer.</ref> ...studied by classifying the ([[connected (topology)|connected]]) manifolds in each dimension separately: ...

In the [[mathematics|mathematical]] fields of [[topology]] and [[K-theory]], the '''Serre–Swan theorem''', also called '''Swan's the ...a)|characteristic]]). The complementary variant stated by [[Richard Swan]] in 1962 is more analytic, and concerns ([[real number|real]], [[complex number ...