Spectral geometry for the Jacobi operator of the identity map


Let (M,g) be a compact Riemannian manifold. We denote by JM the Jacobi operator of the identity map which is a second order elliptic differential operator. In this paper we study the following problem: which geometric properties are determined by the spectrum Spec{JM}?

DOI Code: 10.1285/i15900932v28n1p29

Keywords: harmonic map; identity map; isospectrality; Jacobi operator

Classification: 58J50; 58J53; 53C25; 53C45

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