A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line
A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line
复制标题
流形估值的乘积公式及其在四元数线积分几何中的应用
DOI：
10.4171/cmh/150
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发表时间：
2006
影响因子：
0.9
通讯作者：
A. Bernig
中科院分区：
文献类型：
--
作者：
A. Bernig
流形上光滑赋值的Alesker—Poincare配对用作用于球束上的Rumin微分算子表示。证明了导数算子、签名算子和作用于光滑赋值的拉普拉斯算子对该对在形式上是自伴随的。作为应用，给出了四元数线上SU(2)-与平移不变赋值空间的乘积结构。给出并证明了四元数直线H上的主运动学公式。
The Alesker�Poincare pairing for smooth valuations on manifolds is expressed in terms of the Rumin differential operator acting on the cosphere-bundle. It is shown that the derivation operator, the signature operator and the Laplace operator acting on smooth valuations are formally self-adjoint with respect to this pairing. As an application, the product structure of the space of SU(2)- and translation invariant valuations on the quaternionic line is described. The principal kinematic formula on the quaternionic line H is stated and proved.