Envelopes of families of Legendre mappings in the unit tangent bundle over the Euclidean space
Envelopes of families of Legendre mappings in the unit tangent bundle over the Euclidean space
复制标题
欧几里得空间上单位切丛中勒让德映射族的包络
DOI：
10.1016/j.jmaa.2018.12.057
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发表时间：
2019
影响因子：
1.3
通讯作者：
Takahashi Masatomo
中科院分区：
文献类型：
--
作者：
Tadayuki Watanabe;Takahashi Masatomo
对于具有奇异点的超曲面族，包络的经典定义是模糊的。为了定义具有奇点的超曲面族的包络，我们考虑欧氏空间上单位切丛中的参数前部族和Legendre映射族。我们定义了勒让德映射的热参数族的包络。那么信封也是正面的。我们研究了包络的性质。作为应用，我们给出了一阶偏微分方程奇异解的投影是包络的条件。
For families of hypersurfaces with singular points, a classical definition of an envelope is vague. In order to define an envelope for a family of hypersurfaces with singular points, we considerr-parameter families of frontals and of Legendre mappings in the unit tangent bundle over the Euclidean space. We define an envelope for ther-parameter family of Legendre mappings. Then the envelope is also a frontal. We investigate properties of the envelopes. As an application, we give a condition that the projection of a singular solution of a first order partial differential equation is an envelope.