Holomorphic Legendrian curves in ▫$\mathbb{CP}^3$▫ and superminimal surfaces in ▫$\mathbb{S}^4$▫
Alarcón, Antonio ; Forstnerič, Franc, 1958- ; Lárusson, Finnur
V članku je dokazan Rungejev aproksimacijski izrek za holomorfne Legendrove krivulje in imerzije v kompleksnem projektivnem 3-prostoru ▫$\mathbb{CP}^3$▫ iz odprtih in tudi iz kompaktnih Riemannovih ...ploskev. Dokazano je, da je prostor Legendrovih imerzij odprte Riemannove ploskve v ▫$\mathbb{CP}^3$▫ povezan s potmi. Nadalje je dokazano, da holomorfne Legendrove imerzije iz odprte Riemannove ploskve končnega roda in največ števno mnogo robnimi krivuljami zadoščajo lastnosti Calabi-Yau. S pomočjo tvistorske projekcije in Bryantove korespondence odtod sledijo analogni rezultati za superminimalne ploskve v 4-sferi ▫$\mathbb S^4$▫ s sferično metriko.
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