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Pu's inequality
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Pu's inequality : ウィキペディア英語版
Pu's inequality

In differential geometry, Pu's inequality is an inequality proved by Pao Ming Pu for the systole of an arbitrary Riemannian metric on the real projective plane RP2.
==Statement==
A student of Charles Loewner's, P.M. Pu proved in a 1950 thesis that every metric on the real projective plane \mathbb^2 satisfies the optimal inequality
: \operatorname^2 \leq \frac \operatorname(\mathbb^2),
where sys is the systole. The boundary case of equality is attained precisely when the metric is of constant Gaussian curvature.

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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