$5/2$ -尖边的几何不变量
Geometric invariants of $5/2$-cuspidal edges
摘要：
在$5/2$ -尖边上引入了两个不变量，即次尖曲率和偏差，并研究了它们的基本性质。虽然二次尖点曲率是（普通）尖点边缘的尖点曲率的模拟，但没有对应于偏差的不变量。证明了次尖曲率与极限法曲率的乘积（称为次积曲率）是一个内禀不变量。利用这种内在性，我们表明，任何真正的解析$5/2$尖点边缘与非零限制法曲率承认非平凡的等距变形，这提供了各种不变量的extrinsity。
英文摘要：
We introduce two invariants called the secondary cuspidal curvature and the bias on $5/2$-cuspidal edges, and investigate their basic properties. While the secondary cuspidal curvature is an analog of the cuspidal curvature of (ordinary) cuspidal edges, there are no invariants corresponding to the bias. We prove that the product (called the secondary product curvature) of the secondary cuspidal curvature and the limiting normal curvature is an intrinsic invariant. Using this intrinsity, we show that any real analytic $5/2$-cuspidal edges with non-vanishing limiting normal curvature admits non-trivial isometric deformations, which provide the extrinsity of various invariants.
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