Two kernel vanishing theorems and an estimation theorem for the smallest eigenvalue of the Hodge — de Rham Laplacian

Abstract

In this paper, we formulate two theorems on the disap­pearance of the kernel of the Hodge — de Rham Laplacian and refine the estimate for its smallest eigenvalue on closed Riemannian manifolds.

Keywords

• riemannian manifold
• exterior differential form
• hodge — de rham laplacian
• kernel vanishing theorem
• smallest eigenvalue