In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety...

In relativity and in pseudo-Riemannian geometry, a null hypersurface is a hypersurface whose normal vector at every point is a null vector (has zero length...

In algebraic geometry, a Coble hypersurface is one of the hypersurfaces associated to the Jacobian variety of a curve of genus 2 or 3 by Arthur Coble....

geometry, a Dupin hypersurface is a submanifold in a space form, whose principal curvatures have globally constant multiplicities. A hypersurface is called a...

(quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension...

can be viewed as the equation of an hypersurface, and the solutions of the equation are the points of the hypersurface that have integer coordinates. This...

polynomial F is non-differentiable is called its associated tropical hypersurface, denoted V ( F ) {\displaystyle \mathrm {V} (F)} (in analogy to the vanishing...

In algebraic geometry, given a projective algebraic hypersurface C {\displaystyle C} described by the homogeneous equation f ( x 0 , x 1 , x 2 , … ) =...

differential geometry, complex lamellar vector fields are more often called hypersurface-orthogonal vector fields. They can be characterized in a number of different...

variables x1, x2 and x3. For higher values of n, the level set is a level hypersurface, the set of all real-valued roots of an equation in n > 3 variables....

mathematics, a cubic form is a homogeneous polynomial of degree 3, and a cubic hypersurface is the zero set of a cubic form. In the case of a cubic form in three...

coordinate system we may speak of coordinate planes. Similarly, coordinate hypersurfaces are the (n − 1)-dimensional spaces resulting from fixing a single coordinate...

In mathematics, a Dold manifold is one of the manifolds P ( m , n ) = ( S m × C P n ) / τ {\displaystyle P(m,n)=(S^{m}\times \mathbb {CP} ^{n})/\tau }...

Minkowski Fractal Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex...

_{i=1}^{n}a_{i}{x_{i}}^{m}\ } for some degree m. Such forms F, and the hypersurfaces F = 0 they define in projective space, are very special in geometric...

Minkowski Fractal Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex...

Minkowski Fractal Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex...

an equivalent way to describe the shape operator (denoted by S) of a hypersurface, I I ( v , w ) = ⟨ S ( v ) , w ⟩ n = − ⟨ ∇ v n , w ⟩ n = ⟨ n , ∇ v w...

of n projective hypersurfaces has codimension n, then the degree of the intersection is the product of the degrees of the hypersurfaces. The degree of...

edges and the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells, meeting at right angles...

of arbitrary dimension. Like a plane in space, a hyperplane is a flat hypersurface, a subspace whose dimension is one less than that of the ambient space...

the Lüroth quartics form an open subset of a degree 54 hypersurface, called the Lüroth hypersurface, in the space P14 of all quartics. Böhning & von Bothmer...

n} ⁠-dimensional spherical geometry. Considered extrinsically, as a hypersurface embedded in ⁠ ( n + 1 ) {\displaystyle (n+1)} ⁠-dimensional Euclidean...

three elements generate an abelian quasigroup. "CH" stands for cubic hypersurface. Manin, Yuri Ivanovich (1986) [1972], Cubic forms, North-Holland Mathematical...

problem with two classes, a decision boundary or decision surface is a hypersurface that partitions the underlying vector space into two sets, one for each...

of common points over an algebraically closed field of n projective hypersurfaces defined by homogeneous polynomials in n + 1 indeterminates, then N is...

even-dimensional phase space of a mechanical system or constant-energy hypersurface, which, being codimension one, has odd dimension. Like symplectic geometry...

Minkowski Fractal Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex...

zero. The gradient of F is then normal to the hypersurface. Similarly, an affine algebraic hypersurface may be defined by an equation F(x1, ..., xn) =...

are a conjecture on existence of minimal hypersurfaces and on the spectral geometry of minimal hypersurfaces. In 1978, by studying the complex Monge–Ampère...