Euler Characteristic of Epi-Lipschitz Subsets of Riemannian Manifolds
Euler Characteristic of Epi-Lipschitz Subsets of Riemannian Manifolds
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发表时间：
2013
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通讯作者：
S. Hosseini;M. R. Pouryayevali
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作者：
S. Hosseini;M. R. Pouryayevali
本文给出了完备黎曼流形上epi-Lipschitz子集的切锥和法锥的一些性质。证明了完备黎曼流形的epi-Lipschitz子集是绝对邻域收缩。引入完备黎曼流形的epi-Lipschitz子集的Euler特征线的概念。此外，我们提供了一个充分条件，确保这类集的欧拉特征等于一。然后，将这些结果应用于完备可平行化黎曼流形上的平衡理论。
In this paper we present some properties of tangent and normal cones of epi-Lipschitz subsets of complete Riemannian manifolds. The fact that epi-Lipschitz subsets of complete Riemannian manifolds are absolute neighborhood retracts is proved. A notion of Euler characteristic of epi-Lipschitz subsets of complete Riemannian manifolds is introduced. Moreover, we provide a sufficient condition which ensures that the Euler characteristic of this class of sets is equal to one. Then, these results are applied to equilibrium theory on complete parallelizable Riemannian manifolds.