Absolute curvature measures, II
Absolute curvature measures, II
复制标题
绝对曲率测量，II
DOI：
--
复制
发表时间：
1992
期刊：
影响因子：
--
通讯作者：
M. Zähle
中科院分区：
文献类型：
--
作者：
W. Rother;M. Zähle
在[7]中引入的Rd中的正到达集合的绝对曲率测度满足以下运动学关系：它们在与匀速运动的p平面的交点（或在其上的切向投影）上的积分值是主集合的相应绝对曲率测度的常数倍。在凸体的特殊情况下，第一个结果是所谓的克罗夫顿公式。在光滑流形的微分几何中，有符号曲率测度的类似物是众所周知的，但是那里使用的绝对曲率的运动并不导致这个性质。对于光滑紧致超流形的特殊情形，我们的绝对曲率测度与Santaló [4]用其他方法引入的绝对曲率测度一致.在附录中，我们将截面公式应用于运动不变随机集.
The absolute curvature measures for sets of positive reach in Rd introduced in [7] satisfy the following kinematic relations: Their integrated values on the intersections with (or on the tangential projections onto) uniformly moved p-planes are constant multiples of the corresponding absolute curvature measures of the primary set. In the special case of convex bodies the first result is the so-called Crofton formula. An analogue for signed curvature measures is well known in the differential geometry of smooth manifolds, but the motion of absolute curvatures used there does not lead to this property. For the special case of smooth compact hypermanifolds our absolute curvature measures agree with those introduced by Santaló [4] with other methods.In the appendix, the section formula is applied to motion invariant random sets.