现代几何的结构和领域 Modern geometric structures and fields
子流形高斯像的几何与拓扑是整体微分几何领域的重要研究课题之一。
It plays an important role in global differential geometry to study the geometric and topological properties of Gaussian image of submanifolds.
所有中国人都应该为中国数学家在微分几何领域所取得的成就，和对庞加莱猜测的贡献而感到骄傲。
All Chinese can be proud of the achievements of their mathematicians in differential geometry and their contributions to the completion of the proof of Poincare conjecture.
在数学学科的很多的领域中算术只是起到次要作用，例如逻辑学和几何学。
There are entire fields of mathematics where numerical manipulation is peripheral: logic and geometry, for example.
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