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Wirtinger inequality (2-forms) : ウィキペディア英語版
Wirtinger inequality (2-forms)
: ''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 M, the exterior kth power of the symplectic form (Kähler form) ω, when evaluated on a simple (decomposable) (2k)-vector ζ of unit volume, is bounded above by k!. That is,
: \omega^k(\zeta) \leq k !\,.
In other words, \textstyle} is a calibration on M . An important corollary is that every complex submanifold of a Kähler manifold is volume minimizing in its homology class.
==See also==

*2-form
*Gromov's inequality for complex projective space
*Systolic geometry

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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