About: Gromov's inequality for complex projective space

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In Riemannian geometry, Gromov's optimal stable 2-systolic inequality is the inequality , valid for an arbitrary Riemannian metric on the complex projective space, where the optimal bound is attainedby the symmetric Fubini–Study metric, providing a natural geometrisation of quantum mechanics. Here is the stable 2-systole, which in this case can be defined as the infimum of the areas of rational 2-cycles representing the class of the complex projective line in 2-dimensional homology. The inequality first appeared in as Theorem 4.36.

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  • In Riemannian geometry, Gromov's optimal stable 2-systolic inequality is the inequality , valid for an arbitrary Riemannian metric on the complex projective space, where the optimal bound is attainedby the symmetric Fubini–Study metric, providing a natural geometrisation of quantum mechanics. Here is the stable 2-systole, which in this case can be defined as the infimum of the areas of rational 2-cycles representing the class of the complex projective line in 2-dimensional homology. The inequality first appeared in as Theorem 4.36. The proof of Gromov's inequality relies on the Wirtinger inequality for exterior 2-forms. (en)
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  • In Riemannian geometry, Gromov's optimal stable 2-systolic inequality is the inequality , valid for an arbitrary Riemannian metric on the complex projective space, where the optimal bound is attainedby the symmetric Fubini–Study metric, providing a natural geometrisation of quantum mechanics. Here is the stable 2-systole, which in this case can be defined as the infimum of the areas of rational 2-cycles representing the class of the complex projective line in 2-dimensional homology. The inequality first appeared in as Theorem 4.36. (en)
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  • Gromov's inequality for complex projective space (en)
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