doubly covering manifold

例句：

1. 1. This mathematical model is a double-covering manifold, which can be used to describe the complex behavior of fluids.
   这个数学模型是一个双重覆盖的流形，可以用来描述流体复杂的行为。
2. 2. The research on this double-covering manifold has provided new insights into the study of fluid dynamics.
   对这种双重覆盖的流形的研究为流体动力学的研究提供了新的见解。
3. 3. In the field of computational geometry, the double-covering manifold is apowerful tool for solving complex geometric problems.
   在计算几何领域，双重覆盖的流形是解决复杂几何问题的强大工具。