Wirtinger inequality (2-forms)

From Wikipedia, the free encyclopedia
Jump to: navigation, search
For other inequalities named after Wirtinger, see Wirtinger's inequality.

In mathematics, the Wirtinger inequality for 2-forms, named after Wilhelm Wirtinger, states that on a Kähler manifold , the exterior th power of the symplectic form (Kähler form) ω, when evaluated on a simple (decomposable) -vector ζ of unit volume, is bounded above by . That is,

In other words, is a calibration on . An important corollary is that every complex submanifold of a Kähler manifold is volume minimizing in its homology class.

See also[edit]