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  • Complex manifold — In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk[1] in Cn, such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense… …   Wikipedia

  • Tangent space — In mathematics, the tangent space of a manifold is a concept which facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector pointing from… …   Wikipedia

  • Tangent half-angle formula — In various applications of trigonometry, it is useful to rewrite the trigonometric functions (such as sine and cosine) in terms of rational functions of a new variable t . These identities are known collectively as the tangent half angle formulae …   Wikipedia

  • Complex plane — Geometric representation of z and its conjugate in the complex plane. The distance along the light blue line from the origin to the point z is the modulus or absolute value of z. The angle φ is the argument of z. In mathematics …   Wikipedia

  • Complex projective space — The Riemann sphere, the one dimensional complex projective space, i.e. the complex projective line. In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a …   Wikipedia

  • Complex logarithm — A single branch of the complex logarithm. The hue of the color is used to show the arg (polar coordinate angle) of the complex logarithm. The saturation (intensity) of the color is used to show the modulus of the complex logarithm. The page with… …   Wikipedia

  • Complex multiplication — This article is about certain endomorphism rings. For information about multiplication of complex numbers, see complex numbers. In mathematics, complex multiplication is the theory of elliptic curves E that have an endomorphism ring larger than… …   Wikipedia

  • Complex geodesic — In mathematics, a complex geodesic is a generalization of the notion of geodesic to complex spaces. Definition Let (X, || ||) be a complex Banach space and let B be the open unit ball in X. Let Δ denote the open unit disc in the complex …   Wikipedia

  • Complex argument (continued fraction) — In analysis, the complex argument theta; = arg( z ) is commonly defined as an angle, often in terms of the inverse tangent function, or the inverse cosine. In a purely formal and perfectly rigorous treatment of the complex numbers, such reliance… …   Wikipedia

  • Almost complex manifold — In mathematics, an almost complex manifold is a smooth manifold equipped with smooth linear complex structure on each tangent space. The existence of this structure is a necessary, but not sufficient, condition for a manifold to be a complex… …   Wikipedia

  • Generalized complex structure — In the field of mathematics known as differential geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic structure. Generalized complex structures… …   Wikipedia

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