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In differential geometry, normal coordinates at a point p in a differentiable manifold equipped with a symmetric affine connection are a local coordinate...

integrated must be Riemann integrable on the domain, which is true (for instance) if the function is continuous. If the domain D is normal with respect to...

the concepts in the mid-17th century, though the actual term "polar coordinates" has been attributed to Gregorio Fontana in the 18th century. The initial...

general relativity Normal coordinates Systolic geometry Riemann–Cartan geometry in Einstein–Cartan theory (motivation) Riemann's minimal surface Reilly...

_{rm}^{r}).} By evaluating the δ Γ {\displaystyle \delta \Gamma } s in Riemann normal coordinates, 6 individual terms vanish. 6 further terms combine when manipulated...

normal coordinates (u, v) as ds2 = du2 + dv2 − K(u dv – v du)2/12 + …. Taking a coordinate change from normal coordinates at p to normal coordinates at...

topologically a sphere. Hence the complex projective line is also known as the Riemann sphere (or sometimes the Gauss sphere). It is in constant use in complex...

calculus, founded by Gauss, Riemann, Ricci, and Levi-Civita. Vector and tensor calculus in general curvilinear coordinates is used in tensor analysis on...

divisors on a compact Riemann surface X is the free abelian group on the points of X. Equivalently, a divisor on a compact Riemann surface X is a finite...

rigorously formalized, using limits, by Riemann. Although all bounded piecewise continuous functions are Riemann-integrable on a bounded interval, subsequently...

ξ {\displaystyle \xi } represents: the original Riemann Xi function the modified definition of Riemann xi function, as denoted by Edmund Landau the extent...

connection, and the Riemann curvature via the Levi-Civita connection. Arguably, the definitions directly using local coordinates are preferable, since...

Riemann refers to not only colors and the locations of objects in space, but also the possible shapes of a spatial figure. Using induction, Riemann constructs...

primitive and geometry is established analytically in terms of numerical coordinates. In an axiomatic formulation of Euclidean geometry, such as that of Hilbert...

corollary to the Riemann–Roch theorem: a non-singular curve C of genus g embedded in projective space of dimension g − 1 as a linearly normal curve of degree...

{\displaystyle T(S)} may be regarded as an isomorphism class of "marked" Riemann surfaces, where a "marking" is an isotopy class of homeomorphisms from...

f(z) be analytic is that u and v be differentiable and that the Cauchy–Riemann equations be satisfied: u x = v y , v x = − u y . {\displaystyle u_{x}=v_{y}...

Arthur Cayley, William Rowan Hamilton, Ludwig Schläfli and Bernhard Riemann. Riemann's 1854 Habilitationsschrift, Schläfli's 1852 Theorie der vielfachen...

are homogeneous coordinates on CP1; the point [1:0] corresponds to the point ∞ of the Riemann sphere. By using homogeneous coordinates, many calculations...

restricted places. The last two parts were consciously modelled on the Riemann zeta function, a kind of generating function for prime integers, which...