space-time curvature

The shape of the curve in the wellbore trajectory of horizontal wells is a complex three-dimensional space curve of arbitrary curvature and torsion. Its curved shape greatly affects the status of the column by the force and analysis of the follow-up column mechanics.

水平井全井井眼轨迹曲线形状是一条复杂的具有任意曲率和挠率的三维空间曲线，其弯曲形态极大地影响了管柱的受力状况和对后续的管柱力学的分析计算。

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On the Ruled Hypersurface of a Constant Curvature Space

常曲率空间中的超直纹面

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A. Einstein took the gravitation phenomenon as the curvature property of Riemannian space, the physics phenomenon may be considered as geometry phenomenon. Therefore, Riemannian geometry may be applied in general relativity theory and theoretical physics.

A.Einstein把引力现象解释成黎曼空间的曲率性质，使得物理现象变成几何现象，从而使黎曼几何在广义相对论和理论物理中得到了广泛的应用。

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By means of differential geometry, this article recognizes tensor field on manifold and its covered vector field, scalar field further, at the same time uncovers and depicts the inherent proper curvature meaning of the relativity background space-time ( IR~ 4,η).

从近代微分几何角度，进一步认识张量场及其所涵盖的标量场和矢量场，揭示刻画相对论时空背景的内禀曲率意义；

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Matter, energy and dark energy all produce curvature in space-time , however.

而事实上,物质 、 能量和暗能量在时空中都会产生弯曲.

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At last, the location and 3D shape of the pipeline is reconstructed by the use of the space curve fitting method, which is based on curvature information of discrete points.

然后运用基于等距离离散点曲率信息的空间曲线重建方法重建出管道的空间位置形状。

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Two well-known general relativistic effects due to space-time curvature by mass and charge or angular momentum of a star are deflection of light and radar echo delay.

星体的质量、电量或角动量都会产生时空弯曲，它的两个重要的广义相对论效应就是光线偏折和雷达回波延迟。

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A visual demonstration shows how space-time undergoes curvature when mass is introduced.

可视化演示显示了如何 时空 经历曲率当大众介绍.

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The Casimir energy is a kind of zero-point energy of quantized fields and can be considered as the energy of vacuum polarization of quantized fields due to the presence of boundaries, the curvature of the space-time manifold or some background fields.

Casimir能量是量子场的一类零点能，是由于边界的出现、时空的弯曲以及某些背景场的存在而引起的。

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Complete space-like hypersurfaces with constant mean curvature in locally symmetric Lorentz spaces

局部对称Lorentz空间中具有常平均曲率的完备类空超曲面

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