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  2. Quadric (algebraic geometry) - Wikipedia

    en.wikipedia.org/wiki/Quadric_(algebraic_geometry)

    A smooth quadric over a field k is a projective homogeneous variety for the orthogonal group (and for the special orthogonal group), viewed as linear algebraic groups over k. Like any projective homogeneous variety for a split reductive group, a split quadric X has an algebraic cell decomposition, known as the Bruhat decomposition. (In ...

  3. Hypersurface - Wikipedia

    en.wikipedia.org/wiki/Hypersurface

    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 of dimension n − 1, which is embedded in an ambient space of dimension n, generally a Euclidean space, an affine space or a projective space. [1]

  4. Complex lamellar vector field - Wikipedia

    en.wikipedia.org/wiki/Complex_lamellar_vector_field

    In vector calculus, a complex lamellar vector field is a vector field which is orthogonal to a family of surfaces. In the broader context of differential geometry, complex lamellar vector fields are more often called hypersurface-orthogonal vector fields. They can be characterized in a number of different ways, many of which involve the curl.

  5. Projection formula - Wikipedia

    en.wikipedia.org/wiki/Projection_formula

    Printable version; In other projects ... In algebraic geometry, the projection formula states the following: [1] [2] ... and a locally free -module of ...

  6. Projection (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Projection_(linear_algebra)

    A square matrix is called a projection matrix if it is equal to its square, i.e. if =. [2]: p. 38 A square matrix is called an orthogonal projection matrix if = = for a real matrix, and respectively = = for a complex matrix, where denotes the transpose of and denotes the adjoint or Hermitian transpose of .

  7. Differential geometry of surfaces - Wikipedia

    en.wikipedia.org/wiki/Differential_geometry_of...

    The orthogonal projection of this vector onto T c(t) S defines the covariant derivative ∇ c ′(t) X. Although this is a very geometrically clean definition, it is necessary to show that the result only depends on c ′( t ) and X , and not on c and X ; local parametrizations can be used for this small technical argument.

  8. Fano variety - Wikipedia

    en.wikipedia.org/wiki/Fano_variety

    The adjunction formula implies that K D = (K X + D)| D = (−(n+1)H + deg(D)H)| D, where H is the class of a hyperplane. The hypersurface D is therefore Fano if and only if deg(D) < n+1. More generally, a smooth complete intersection of hypersurfaces in n-dimensional projective space is Fano if and only if the sum of their degrees is at most n.

  9. Rindler coordinates - Wikipedia

    en.wikipedia.org/wiki/Rindler_coordinates

    Because the Rindler observers are vorticity-free, they are also hypersurface orthogonal. The orthogonal spatial hyperslices are t = t 0 {\displaystyle t=t_{0}} ; these appear as horizontal half-planes in the Rindler chart and as half-planes through T = X = 0 {\displaystyle T=X=0} in the Cartesian chart (see the figure above).