Pu's inequality
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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. A student of Charles Loewner''s, P.M. Pu proved in a 1950 thesis (published in 1952) that every metric on the real projective plane mathbb{RP}^2 satisfies the optimal inequality operatorname{sys}^2 leq frac{pi}{2} operatorname{area}(mathbb{RP}^2), where sys is the systole. The boundary case of equality is…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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. A student of Charles Loewner''s, P.M. Pu proved in a 1950 thesis (published in 1952) that every metric on the real projective plane mathbb{RP}^2 satisfies the optimal inequality operatorname{sys}^2 leq frac{pi}{2} operatorname{area}(mathbb{RP}^2), where sys is the systole. The boundary case of equality is attained precisely when the metric is of constant Gaussian curvature.