Behavior of Gaussian Curvature and Mean Curvature Near Non-degenerate Singular Points on Wave Fronts
Behavior of Gaussian Curvature and Mean Curvature Near Non-degenerate Singular Points on Wave Fronts
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波前非简并奇异点附近的高斯曲率和平均曲率行为
DOI：
10.1007/978-4-431-56021-0_14
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Masaaki Umehara and Kotaro Yamada
中科院分区：
文献类型：
--
作者：
Luciana F;Martins;Kentaro Saji;Masaaki Umehara and Kotaro Yamada
We define cuspidal curvature(resp. normalized cuspidal curvature) along cuspidal edges (resp. at a swallowtail singularity) in Riemannian 3-manifolds, and show that it gives a coefficient of the divergent term of the mean curvature function. Moreover, we show that the productcalled the product curvature (resp.called normalized product curvature) of(resp.) and the limiting normal curvatureis an intrinsic invariant of the surface, and is closely related to the boundedness of the Gaussian curvature. We also consider the limiting behavior ofwhen cuspidal edges accumulate to other singularities. Moreover, several new geometric invariants of cuspidal edges and swallowtails are given.
