We prove that the Lawson surface $\xi_{g,1}$ in Lawson’s original notation, which has genus $g$ and can be viewed as a desingularization of two orthogonal great two-spheres in the round three-sphere $\mathbb{S}^3$, has index $2g + 3$ and nullity $6$ for any genus $g \geq 2$. In particular $\xi_{g,1}$ has no exceptional Jacobi fields, which means that it cannot “flap its wings” at the linearized level and is $C^1$-isolated.

中文翻译：

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Lawson的索引和无效表面$ \ xi_ {g，1} $

我们证明了Lawson原始符号中的Lawson曲面$ \ xi_ {g，1} $，具有$ g $属类，可以看作是圆形三球$ \ mathbb {中两个正交的大二球的分解。 S} ^ 3 $，对于任何属$ g \ geq 2 $具有索引$ 2g + 3 $和无效值$ 6 $。特别是$ \ xi_ {g，1} $没有特殊的Jacobi字段，这意味着它不能在线性化的水平上“扇动翅膀”并且是$ C ^ 1 $隔离的。