On the spectral geometry of minimal submanifolds in a quaternionic space form (Q2782754)

Let \(N^{4n}(c)\) be the \(4n\)-dimensional quaternionic space form of constant quaternionic sectional curvature \(c\), and let \(M\) be a minimal submanifold of \(N\).NEWLINENEWLINENEWLINEThe purpose of the present paper is to study the spectral geometry of the normal Jacobi operator \(J\) associated to the immersion of \(M\) in \(N\), when \(M\) is totally complex or totally real. Using the asymptotic expansion of the trace of \(e^{-tJ}\) [see \textit{P. Gilkey}, ``Invariance theory, the heat equation and the Atiyah-Singer index theorem'', Publish or Perish (1984; Zbl 0565.58035)] the authors first determine some spectral invariants of \(J\) (for the codimension not equal to \(6\)). Then they draw a number of geometric conclusions from the isospectral condition \(\text{Spec}(M,J)=\text{Spec}(M',J')\).