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- W3123324750 abstract "In the round 6-sphere, null-torsion holomorphic curves are fundamental examples of minimal surfaces. This class of minimal surfaces is quite rich: By a theorem of Bryant, extended by Rowland, every closed Riemann surface may be conformally embedded in the round 6-sphere as a null-torsion holomorphic curve. In this work, we study the second variation of area for compact null-torsion holomorphic curves $$Sigma $$ of genus g and area $$4pi d$$ , focusing on the spectrum of the Jacobi operator. We show that if $$g le 6$$ , then the multiplicity of the lowest eigenvalue $$lambda _1 = -2$$ is equal to 4d. Moreover, for any genus, we show that the nullity is at least $$2d + 2 - 2g$$ . These results are likely to have implications for the deformation theory of asymptotically conical associative 3-folds in $${mathbb {R}}^7$$ , as studied by Lotay." @default.
- W3123324750 created "2021-02-01" @default.
- W3123324750 creator A5085486195 @default.
- W3123324750 date "2022-09-22" @default.
- W3123324750 modified "2023-09-27" @default.
- W3123324750 title "The Second Variation for Null-Torsion Holomorphic Curves in the 6-Sphere" @default.
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- W3123324750 doi "https://doi.org/10.1007/s12220-022-01040-9" @default.
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