允许强凸斜率度量的旋转曲面
Surfaces of revolution admitting strongly convex slope metrics
摘要：
本文讨论了具有斜率度量的曲面的几何性质。得到了任意旋转曲面允许强凸斜率度量的充要条件。这样的条件涉及笛卡尔坐标和极坐标上的相关函数的导数的某些不等式。特别地，我们将这个结果应用到某些众所周知的旋转曲面。
英文摘要：
This paper discusses the geometry of a surface endowed with a slope metric. We obtain necessary and sufficient conditions for any surface of revolution to admit a strongly convex slope metric. Such conditions involve certain inequalities for the derivative of the associated function on the Cartesian coordinate and the polar coordinate. In particular, we apply this result to certain well-know surface of revolution.
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