various splitting theorems on when a pseudo-Riemannian manifold can be given as a metric product. The best-known is the Cheeger–Gromoll splitting theorem for...

Splitting, railway operation Heegaard splitting Splitting field Splitting principle Splitting theorem Splitting lemma for the numerical method to solve...

theory of causal structure on Lorentzian manifolds, Geroch's theorem or Geroch's splitting theorem (first proved by Robert Geroch) gives a topological characterization...

The Chebotarev density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field Q...

In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial...

also in the non-regular case, one can use Weinstein splitting theorem (or Darboux-Weinstein theorem). It states that any Poisson manifold ( M n , π ) {\displaystyle...

theorem (proof theory) Deduction theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

follows from Waldhausen's Theorem that every reducible splitting of an irreducible manifold is stabilized. A Heegaard splitting is weakly reducible if there...

specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients...

constant Cheeger constant (graph theory) Cheeger–Müller theorem soul theorem splitting theorem Collapsing manifold L² cohomology Riemannian geometry Faculty...

T)+\dim(\operatorname {Ker} T)=\dim(\operatorname {Domain} (T)).} This theorem can be refined via the splitting lemma to be a statement about an isomorphism of spaces...

equality if and only if the Riemannian manifold is a flat torus. Splitting theorem. If a complete n-dimensional Riemannian manifold has nonnegative Ricci...

this class is flat, which is a corollary of Cheeger and Gromoll's splitting theorem. On a simply-connected Kähler manifold, a Kähler metric is Ricci-flat...

Hobby–Rice theorem, and it is used to get an exact division of a cake. Each problem can be solved by the next problem: Discrete splitting can be solved...

Arrow's impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the...

primitive element theorem states that every finite separable field extension is simple, i.e. generated by a single element. This theorem implies in particular...

the key point in the proof of Gromov's compactness theorem. The Cheeger–Gromoll splitting theorem states that if a complete Riemannian manifold ( M ,...

Vampire is an automatic theorem prover for first-order classical logic developed in the Department of Computer Science at the University of Manchester...

Biography portal Physics portal Geroch energy Geroch group Geroch's splitting theorem GHP formalism American Men and Women of Science, Thomson Gale, 2004...

In mathematics, the Gershgorin circle theorem may be used to bound the spectrum of a square matrix. It was first published by the Soviet mathematician...

In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there...

The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...

In mathematics, Brown's representability theorem in homotopy theory gives necessary and sufficient conditions for a contravariant functor F on the homotopy...

and Miguel Sánchez, " On smooth Cauchy hypersurfaces and Geroch's splitting theorem", Communications in Mathematical Physics 243 (2003), no. 3, 461–470...

In the analysis of algorithms, the master theorem for divide-and-conquer recurrences provides an asymptotic analysis for many recurrence relations that...

The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior...

splitting theorem says that the splitting of the fundamental group as a maximally noncommutative direct product implies the isometric splitting of the manifold...

transformation are named after him. He also proved the first version of the splitting theorem. Stefan Cohn-Vossen was born 28 May, 1902 to Emanuel Cohn, a lawyer...

Then the splitting principle can be quite useful. One version of the splitting principle is captured in the following theorem. This theorem holds for...