Abstract
In this paper, we study Pizzetti-type formulas for Stiefel manifolds and Cauchy-type formulas for the tangential Dirac operator from a distributional perspective. First we illustrate a general distributional method for integration over manifolds in Rm defined by means of k equations φ1(x_)=…=φk(x_)=0. Next, we apply this method to derive an alternative proof of the Pizzetti formulae for the real Stiefel manifolds SO(m)/SO(m−k). Besides, a distributional interpretation of invariant oriented integration is provided. In particular, we obtain a distributional Cauchy theorem for the tangential Dirac operator on an embedded (m−k)-dimensional smooth surface.
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