In mathematics, a complex torus is a particular kind of complex manifold M whose underlying smooth manifold is a torus in the usual sense (i.e. the cartesian...

is called a torus of revolution, also known as a ring torus. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis...

and Albanese varieties). A complex torus of dimension g is a torus of real dimension 2g that carries the structure of a complex manifold. It can always be...

In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies...

groups over the complex numbers. A connected compact complex Lie group is precisely a complex torus (not to be confused with the complex Lie group C ∗ {\displaystyle...

Stated another way, a torus embedded in R3 is an asymmetric reduced-dimension projection of the maximally symmetric Clifford torus embedded in R4. The relationship...

considers an action of a real or complex torus on a manifold (or an orbifold). A normal algebraic variety with a torus acting on it in such a way that...

and torus admit complex structures but the Möbius strip, Klein bottle and real projective plane do not. Every compact Riemann surface is a complex algebraic...

(real) compact Lie group is a torus; i.e., a Lie group isomorphic to ( S 1 ) h {\displaystyle (S^{1})^{h}} . A connected complex Lie group that is a compact...

itself is orthogonal to that axis. The word "torus" originates from the Latin word "protuberance." Torus fractures are low risk and may cause acute pain...

the definitionpg 30. For a complex torus X = V / Λ {\displaystyle X=V/\Lambda } , where V {\displaystyle V} is a complex vector space of dimension n...

curve. Hodge theory Complex torus Barth, Wolf P.; Hulek, Klaus; Peters, Chris A.M.; Van de Ven, Antonius (2004), Compact Complex Surfaces, Ergebnisse...

Z[i] is the Gaussian integer ring, and θ is any non-zero complex number. Any such complex torus has the Gaussian integers as endomorphism ring. It is known...

In mathematics, a genus g surface (also known as a g-torus or g-holed torus) is a surface formed by the connected sum of g distinct tori: the interior...

polarized abelian variety, of dimension g, and hence, over the complex numbers, it is a complex torus. If p is a point of C, then the curve C can be mapped to...

this happens are hyperelliptic surfaces, finite quotients of a complex torus of complex dimension 2, which have vanishing first integral Chern class but...

rational map f = ΘLΘ−1 from the complex sphere to itself such that Θ is a holomorphic map from a complex torus to the complex sphere and L is an affine map...

In mathematics, an algebraic torus, where a one dimensional torus is typically denoted by G m {\displaystyle \mathbf {G} _{\mathbf {m} }} , G m {\displaystyle...

compact torus. It has been shown that every principal torus bundle over a torus is of this form, see. More generally, a compact nilmanifold is a torus bundle...

3t\end{aligned}}} The (2,3)-torus knot is also a trefoil knot. The following parametric equations give a (2,3)-torus knot lying on torus ( r − 2 ) 2 + z 2 = 1...

of weight 6. The quotient of the complex plane C by the lattice containing all Eisenstein integers is a complex torus of real dimension 2. This is one...

intermediate Jacobian of a compact Kähler manifold or Hodge structure is a complex torus that is a common generalization of the Jacobian variety of a curve and...

Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups. A torus in a compact Lie group G is a compact, connected...

algebraic torus (which is not necessarily compact, in contrast to a complex torus). A k-torus is a torus defined over k. The centralizer of a maximal torus is...

the commutator subgroup is abelian Abelianisation Abelian variety, a complex torus that can be embedded into projective space Abelian surface, a two-dimensional...

group with the real torus given above. In fact, this torus can be equipped with a complex structure, giving the dual complex torus. Explicitly, a line...

The torus is defined as a product of two circles T 2 = S 1 × S 1 {\displaystyle T^{2}=S^{1}\times S^{1}} . The torus has a single path-connected...

Riemann theta function for algebraic curves of arbitrary genus. The complex torus associated to a genus g {\displaystyle g} algebraic curve, obtained...

^{*}} . This is useful when studying complex tori because the character group of the lattice in a complex torus V / Λ {\displaystyle V/\Lambda } is canonically...

variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends...