Spectral geometry of totally complex submanifolds of \(QP^n\) (Q862151)

Let \(M\) be a compact connected closed Riemannian manifold which is isometrically immersed in a Riemannian manifold \(\bar M\). Let \(J\) be the associated \textit{Jacobi operator}; \(J\) is a second order elliptic operator of Laplace type which is often called the \textit{second variation operator}. The author determines the first three terms in the heat trace asymptotics for the Jacobi operator in the setting where \(M\) is a totally complex submanifold of quaternionic projective space \(QP^n\). These invariants together with the corresponding invariants of the Laplace-Beltrami operator are then used to characterize totally complex parallel submanifolds of \(QP^n\).