The Characteristic Values of Laplacian Δ on the Nonorientable Compact C∞ Riemannian Manifolds

Abstract:

      The aim of this paper is to generalize some results of the characteristic values of Laplacian Δ:∧^kM→∧^kM and Liouville Theorem on an n-dimensional orientable compact C^∞ Riemannian manifold (M,g) to a nonorientable manifold applying the orientation cover manifold M, the orthogonal decomposition ∧^kM=∧^kM⁺⊕∧^kM^- and the isomorphism π^*:∧^kM→∧^kM⁺.