A Spectral Condition Determining the Kaehler Property

Spectral Geometry and the Kaehler Condition for Hermitian Manifolds with Boundary

Let (M, g, J) be a compact Hermitian manifold with a smooth boundary. Let ∆p,B and ⊓ ⊔p,B be the realizations of the real and complex Laplacians on p forms with either Dirichlet or Neumann boundary conditions. We generalize previous results in the closed setting to show that (M, g, J) is Kaehler if and only if Spec(∆p,B) = Spec(2 ⊓ ⊔p,B) for p = 0, 1. We also give a characterization of manifold...

A Spectral Equivalent Condition of the P-polynomial Property for Association Schemes

We give two equivalent conditions of the P -polynomial property of a symmetric association scheme. The first equivalent condition shows that the P -polynomial property is determined only by the first and second eigenmatrices of the symmetric association scheme. The second equivalent condition is another expression of the first using predistance polynomials.

On a Spectral Property of Jacobi Matrices

Let J be a Jacobi matrix with elements bk on the main diagonal and elements ak on the auxiliary ones. We suppose that J is a compact perturbation of the free Jacobi matrix. In this case the essential spectrum of J coincides with [−2, 2], and its discrete spectrum is a union of two sequences {xj }, x + j > 2, x − j < −2, tending to ±2. We denote sequences {ak+1 − ak} and {ak+1 + ak−1 − 2ak} by ∂...

Lecture on Kaehler manifolds

A spectral route to determining chirality