Eigenvalues and eigenforms on Calabi-Yau threefolds

We present a numerical algorithm for computing the spectrum of the Laplace-de Rham operator on Calabi-Yau manifolds, extending previous work on the scalar Laplace operator. Using an approximate Calabi-Yau metric as input, we compute the eigenvalues and eigenforms of the Laplace operator acting on (p, q)-forms for the example of the Fermat quintic threefold. We provide a check of our algorithm by computing the spectrum of (p, q)-eigenforms on P3.(c) 2023 Elsevier B.V. All rights reserved.