A comparison theorem for eigenvalues of the covariant Laplacian
The minimax principle is employed to bound the eigenvalues \(\lambda_ n\), of a covariant Laplacian associated to a connection on a vector bundle, above by the eigenvalues \(\mu_ n\), of a corresponding scalar Laplacian. If there exists a non-vanishing eigensection, of the bundle, and \(n=0\), then equality is attained. Some examples are given.
scientific article; zbMATH DE number 4180380
scientific article