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...
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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...
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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....
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geometry, a Dupin hypersurface is a submanifold in a space form, whose principal curvatures have globally constant multiplicities. A hypersurface is called a...
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Quadric (redirect from Quadric hypersurface)
(quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension...
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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...
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Tropical geometry (redirect from Tropical hypersurface)
polynomial F is non-differentiable is called its associated tropical hypersurface, denoted V ( F ) {\displaystyle \mathrm {V} (F)} (in analogy to the vanishing...
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In algebraic geometry, given a projective algebraic hypersurface C {\displaystyle C} described by the homogeneous equation f ( x 0 , x 1 , x 2 , … ) =...
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differential geometry, complex lamellar vector fields are more often called hypersurface-orthogonal vector fields. They can be characterized in a number of different...
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Level set (redirect from Level hypersurface)
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....
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Cubic form (redirect from Cubic hypersurface)
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...
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Coordinate system (redirect from Coordinate hypersurface)
coordinate system we may speak of coordinate planes. Similarly, coordinate hypersurfaces are the (n − 1)-dimensional spaces resulting from fixing a single coordinate...
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Dold manifold (redirect from Dold hypersurface)
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 }...
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Minkowski Fractal Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex...
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Diagonal form (redirect from Fermat hypersurface)
_{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...
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Minkowski Fractal Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex...
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Minkowski Fractal Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex...
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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...
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Degree of an algebraic variety (redirect from Degree of a hypersurface)
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...
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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...
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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...
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Lüroth quartic (redirect from Lüroth hypersurface)
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...
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n} -dimensional spherical geometry. Considered extrinsically, as a hypersurface embedded in ( n + 1 ) {\displaystyle (n+1)} -dimensional Euclidean...
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CH-quasigroup (redirect from Cubic hypersurface quasigroup)
three elements generate an abelian quasigroup. "CH" stands for cubic hypersurface. Manin, Yuri Ivanovich (1986) [1972], Cubic forms, North-Holland Mathematical...
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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...
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of common points over an algebraically closed field of n projective hypersurfaces defined by homogeneous polynomials in n + 1 indeterminates, then N is...
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even-dimensional phase space of a mechanical system or constant-energy hypersurface, which, being codimension one, has odd dimension. Like symplectic geometry...
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Minkowski Fractal Degrees of freedom Polytopes and shapes Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex...
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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) =...
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are a conjecture on existence of minimal hypersurfaces and on the spectral geometry of minimal hypersurfaces. In 1978, by studying the complex Monge–Ampère...
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