Characterizations of some product manifolds by their spectrum (Q814803)

It is proved that \(S^2(c)\times S^2(c'), S^4(c)\times S^4(c')\) and \(\mathbb CP^2(c)\times \mathbb CP^2(c')\) are well identified by their spectra, respectively. Here, \(S^n(c)\) is the \(n\)-dimensional sphere with constant sectional curvature \(c>0\), and \(\mathbb CP^2(c)\) is the complex projective space of complex dimension \(2\) with constant holomorphic sectional curvature \(c>0.\) These results provide new positive examples for the old problem: does the spectrum of a manifold determine its metric?