unconditional. For higher-dimensional spaces, the Weyl–Schouten theorem (named after Hermann Weyl and Jan Arnoldus Schouten) characterizes the existence of isothermal...

see Weyl transformation Weyl tensor Weyl transform Weyl transformation Weyl–Schouten theorem Weyl's criterion Weyl's lemma on hypoellipticity Weyl's lemma...

discovery. Schouten's name appears in various mathematical entities and theorems, such as the Schouten tensor, the Schouten bracket and the Weyl–Schouten theorem...

Projective and Related Structures", Rocky Mountain Journal of Mathematics, vol. 24, Number 4, 1191-1217. Weyl–Schouten theorem Cotton tensor v t e v t e v t e...

transform Weyl transformation Weyl vector of a compact Lie group Weyl–Brauer matrices Weyl−Lewis−Papapetrou coordinates Weyl–Schouten theorem Weyl–von Neumann...

self-dual and antiself-dual parts C+ and C−. The Weyl tensor can also be expressed using the Schouten tensor, which is a trace-adjusted multiple of the...

decomposition Schouten tensor Weyl curvature Ricci flow Einstein manifold Holonomy Gauss–Bonnet theorem Hopf–Rinow theorem Cartan–Hadamard theorem Myers theorem Rauch...

dimension is odd, or it will decompose into a pair of so-called "half-spin" or Weyl representations if the dimension is even. What characterizes spinors and...

Arnoldus Schouten) Schouten tensor, a mathematical object related to differential geometry Schouten–Nijenhuis bracket, mathematical operator Weyl–Schouten theorem...

{\displaystyle 1-{\frac {2GM}{r}}} . Weyl–Schouten theorem conformal geometry Yamabe problem Ray D'Inverno. "6.13 The Weyl tensor". Introducing Einstein's...

then every symmetric parallel 2-tensor is a constant multiple of the metric. Weyl–Schouten theorem Arthur Besse, Einstein Manifolds, Springer (1987)....

Nikolayevsky (2011). "Conformally Osserman manifolds of dimension 16 and a Weyl–Schouten theorem for rank-one symmetric spaces". Annali di Matematica Pura ed Applicata...

^{c}\nabla _{a}P_{bc}} where W {\displaystyle W} is the Weyl tensor, and P {\displaystyle P} the Schouten tensor given in terms of the Ricci tensor R a b {\displaystyle...

independently of Levi-Civita, Jan Arnoldus Schouten obtained analogous results. In the same year, Hermann Weyl generalized Levi-Civita's results. (M, g)...

natural, metric-independent generalization of Stokes' theorem, Gauss's theorem, and Green's theorem from vector calculus. If a differential k-form is thought...

allows expressing the fundamental theorem of calculus, the divergence theorem, Green's theorem, and Stokes' theorem as special cases of a single general...

Schouten 1954, p. 292. do Carmo 2016, p. 301; Eisenhart 1926, Section 40; Schouten 1954, Section VI.2; Struik 1961, Section 5-3. Beltrami 1868; Weyl 1921...

particular importance was Hermann Weyl who made important contributions to the foundations of general relativity, introduced the Weyl tensor providing insight...

n → R {\displaystyle \mathbb {R} ^{n}\to \mathbb {R} } ). Multinomial theorem ( ∑ i = 1 n x i ) k = ∑ | α | = k ( k α ) x α {\displaystyle \left(\sum...

after M. F. Atiyah and I. Singer published their index theorems" Rudin 1991, p. 15 1.18 Theorem Let Λ {\textstyle \Lambda } be a linear functional on a...

include the exterior algebra, the symmetric algebra, the Clifford algebra, the Weyl algebra, and the universal enveloping algebra in general. The exterior algebra...

global geometric and topological information by comparison (cf. comparison theorem) with the geometry of a constant curvature space form. This is since lower...

gauge-invariant. See Einstein–Hilbert action for more information. Noether's theorem implies that there is a conserved current associated with translations...

invariants called the curvature and the torsion of a curve. The fundamental theorem of curves asserts that the knowledge of these invariants completely determines...

Hodge star operator not defined). The identity can be proved from Stokes' theorem for smooth forms: 0   =   ∫ M d ( η ∧ ⋆ ζ )   =   ∫ M ( d η ∧ ⋆ ζ + ( −...

minimizing sequence need not converge to a geodesic. The metric Hopf-Rinow theorem provides situations where a length space is automatically a geodesic space...

(with cutoff at the critical frequency) per the Nyquist–Shannon sampling theorem, the resulting discrete-time signal will be a Kronecker delta function...

{\displaystyle H} a closed subgroup (and thus a Lie subgroup by Cartan's theorem), then the quotient map is a fiber bundle. One example of this is the Hopf...

Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl...

cardinality, which is called the dimension of V. This is the dimension theorem. A generating set S is a basis of V if and only if it is minimal, that...