它进一步说明一个四元流形的截面曲率的估计对许多对称黎曼空间都是有效的。
It proves that the estimate sectional curvature of a quaternion manifold is very useful for Riemann symmetric space.
本文定义了伪黎曼空间型中的旋转超曲面，并给出其参数表达式及主曲率计算公式。
Rotation hypersurfaces in pseudo-Riemannian space forms are defined and their explicit parametrizations are given in the present paper, and their principal curvatures are computed.
本文研究了伪黎曼空间型中具有常平均曲率的类空子流形，得到了这类空子流形的一个积分不等式及刚性定理。
This paper discusses the space-like submanifolds with constant mean curvature in a pseudo-Riemannian space form, and obtain an integrate inequality and a rigidity theorem.
在已知空间物体表面区域方程的前提下，利用黎曼和可以方便地求出被测物体的体积。
It is very convenient to calculate the object volume to use Riemann sum after obtained the object surface region equation.
利用黎曼对称空间同正交对称李代数之间的密切关系及一个矩阵不等式给出了一个复流形上截面曲率的上界的精确估计。
We used the relationship of the Riemann symmetric space and the symmetric algebra, a matrix inequality to provided a estimate sectional curvature of a complex manifold.
通过计算全测地子流形的基本群，确定了紧正规黎曼对称空间的极大的极大秩全测地子流形的整体分类。
In this paper, the authors give the globally classfication of the maximal totally geodesic submanifolds with maximal rank of normal Riemannian symmetric Spaces by computing the fundamental group.
给出了一类黎曼浸没在全空间中第一特征值的下界估计。
In this paper, we present a lower bound for the first eigenvalue of the total Spaces of some class of Riemannian submersions.
在空间相似三角形注视点估计算法的基础上，提出一种基于黎曼几何的视线落点补偿方法 。
One novel gaze point compensation algorithm in Riemannian space was proposed in this paper based on the estimation algorithm of gaze point in space similar triangles.
李三系作为一种代数体系，最初源于对黎曼流形的一类特殊子空间——全测地子流形的研究。
As an algebraic system, Lie triple systems arise upon consideration of certain sub-spaces of Riemannian manifolds, the totally geodesic submanifolds.
在黎曼位形空间中研究了约束多体系统的动力学问题。
The dynamic problem of constrained multibody systems in Riemannian configuration space is researched.
在构造了完备化空间之后，证明了该空间就是勒贝格可积函数空间，从而说明了黎曼积分的完备化形式是勒贝格积分。
After constrcting the perfective space prove that this space is just the space of lebes gue integratiable function thus explain that lebes gue integral is the form of the perfective riemann integral.
给出了一类黎曼浸没在全空间中第一特征值的下界估计。
The lower bound of the first eigenvalue on compact Riemann manifold;
后来发现可以通过引入仿射参数而避开双值性，实质上是将两叶黎曼面分别映射到 仿射参数空间。
The double-valued problem can be simplified by introducing an appropriate affine parameter, namely, mapping the two Riemann sheets on the plane of the spectral parameter to the affine parameter space.
后来发现可以通过引入仿射参数而避开双值性，实质上是将两叶黎曼面分别映射到 仿射参数空间。
The double-valued problem can be simplified by introducing an appropriate affine parameter, namely, mapping the two Riemann sheets on the plane of the spectral parameter to the affine parameter space.
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