Kodai Mathematical Journal

Geometric invariants of 5/2-cuspidal edges

Atsufumi Honda and Kentaro Saji

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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 intrinsicity, we show that any real analytic 5/2-cuspidal edges with non-vanishing limiting normal curvature admit non-trivial isometric deformations, which provides the extrinsicity of various invariants.

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Kodai Math. J., Volume 42, Number 3 (2019), 496-525.

First available in Project Euclid: 31 October 2019

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Honda, Atsufumi; Saji, Kentaro. Geometric invariants of 5/2-cuspidal edges. Kodai Math. J. 42 (2019), no. 3, 496--525. doi:10.2996/kmj/1572487230. https://projecteuclid.org/euclid.kmj/1572487230

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