The purpose of this paper is to prove the Bochner Curvature tensor of Contact Riemannian manifold is an invariant of gauge transformations if and only if the CR-stucture Corresponding to(η,ω) is integrable. 本文证明了在Contact黎曼流形(M.η.g)上,Bochner型曲率张量是Gauge变换的不变量当且仅当对应的Contact-Riemanian结构是可积的。
The Scalar Curvature of the Principal Fibre Bundle with a Right-translation Invariant Metric and the Unified Lagrangian of Gravitational-gauge Fields 主丛右移不变度规下的标曲率和引力&规范场的统一作用量
The mechanical properties on the active surfaces of the molds or dies will be directly influenced by non-uniform distribution of the geometric intrinsic quantities such as curvature, metric invariant, and convexity-concavity of the surfaces. 曲率、度规不变量、凸凹性等几何内蕴量的不均匀分布直接影响模具的力学性能。
Recently, Fung et al ( 1997) pointed out that the normal curvature is not invariant of a uniform change of scale. 最近,Fung(1997)等指出曲率度量不是数据尺度不变量。
Our constantly changing curvature based internal force model is scale invariant. 据此,提出了基于恒定曲率变化的内部力模型。
In the algorithm, first 1D and 2D structural information of the image is extracted by monogenic curvature tensor to improve motion estimation accuracy under uneven illumination by using the advantage of image structure being invariant to illumination change. 在该算法中,先用单演曲率张量来提取图像的1维和2维结构信息,利用图像结构在光照变化下保持不变的优点,提高在光照不均匀条件下的运动估计精度。