100 English words for 'the Riemannian metric for 2-dimensional manifolds, i.e. given a surface with regular parametrization x(u,v), the first fundamental form is a set of three functions, {E, F, G}, dependent on u and v, which give information about local intrinsic curvature of the surface. These functions are given by'

first fundamental form

pseudo-Riemannian manifold

Killing field

Riemannian geometry

Riemannian

Belyi's theorem

curvature

differentiable manifold

Grothendieck-Riemann-Roch theorem

metageometrician

pushforward

Meyer set

space-filling curve

affine differential geometry

Atiyah-Singer index theorem

Euclideanism

Cauchy problem

orthant

Weyl tensor

solid geometry

Ahlfors theory

Euclidian space

rhombicity

differential geometry

Hessian matrix

geodesicity

quasifield

algebrogeometric

affine

three-dimensional

Brouwer fixed-point theorem

cubic

solid torus

metageometry

Riemann space

geometrician

Morse function

geometer

three-dimensional figure

solid figure

hyperbolic function

geometrically

cubinvariant

Einstein space

Riemannian manifold

varifold

Krein-Milman theorem

tetrad

function space

hypergeometry

presymplectic

differential structure

de Sitter space

foliation

Dehn surgery

conicosubulate

non-Euclidean geometry

Menger sponge

algebraic geometer

quaternion

spherics

analytic geometry

point cloud

differential topology

Lefschetz fixed-point theorem

geometricize

tangent space

homotopy

autometry

flat space

tesseract

hypersphere

geometral

stack

Cartesian space

Gaussian curvature

hyperbolic dodecahedron

primitive

Fréchet surface

antilinear

solid

spheroform

slope field

Tschirnhaus transformation

Riemann

hyperbolic sine

Sobolev space

Zeuthen-Segre invariant

linear transformation

Hodge theory

symplectic

quasitoric

geometrographic

complex geometry

natural function

eigenplane