On eigen-values of Laplacian and curvature of Riemannian manifold
On eigen-values of Laplacian and curvature of Riemannian manifold
1. Introduction.Let (M, g) be a compact connected orientable Riemannian manifold with fundamental tensor g y and Δ be the Laplace-Bertrami operator acting on differentiable functions of M, that is,where Vj denotes the covariant differentiation V<?/9ay with respect to the Levi-Civita connection.Let Sp{M, g)= {0 = λ 0 > λi …