Spiral Minimal Products
| Autor: | Li, Haizhong, Zhang, Yongsheng |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | This paper exhibits a structural strategy to produce new minimal submanifolds in spheres based on two given ones. The method is to spin the given minimal submanifolds by a curve $\gamma\subset \mathbb S^3$ in a balanced way and leads to resulting minimal submanifolds $-$ spiral minimal products, which form a two-dimensional family arising from intriguing pendulum phenomena decided by $C$ and $\tilde C$. With $C=0$, we generalize the construction of minimal tori in $\mathbb S^3$ explained in [Bre13] to higher dimensional situations. When $C=-1$, we recapture previous relative work in [CLU06] and [HK12] for special Legendrian submanifolds in spheres, and moreover, can gain numerous $\mathscr C$-totally real and totally real embedded minimal submanifolds in spheres and in complex projective spaces respectively. A key ingredient of the paper is to apply a beautiful extension result of minimal submanifolds by Harvey and Lawson [HL75] for a rotational reflection principle in our situation to establish curve $\gamma$. Comment: Further improved version (52 pages, 10 figures), to be submitted |
| Databáze: | arXiv |
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