An integral formula for the heat kernel of tubular neighborhoods of complete (connected) Riemannian manifolds
The author considers a complete Riemannian manifold \(M\) and a submanifold \(N\) with its normal bundle. Using Fermi coordinates with respect to \(N\) he obtains an integral formula for the Dirichlet heat kernel and so a probabilistic representation for the integral \(\int_N f(y) p^{M_0}_t (x,y)dy\) where \(f\) is any measurable function with compact support on \(M_0\), a tubular neighbourhood on \(N\), and \(p\) is the above heat kernel. This allows the author to obtain heat kernel formulae for the complex projective space \(\mathbb{C} P^n\), the quaternionic projective space \(QP^n\) and the Caley line \(CaP^1\).
scientific article; zbMATH DE number 936750