Eigenvalues Variation of the P-Laplacian Under the Ricci Flow on Sm

Abstract

Abstract. Let (M, F ) be a compact Finsler manifold. Studying the eigenvalues and eigenfunctions for the linear and nonlinear geometric operators is a known problem. In this paper we will consider the eigenvalue problem for the p-laplace operator for Sasakian metric acting on the space of functions on SM . We find the first variation formula for the eigenvalues of p-Laplacian on SM evolving by the Ricci flow on M and give some examples. Kami memperoleh rumus variasi pertama dan memberikan beberapa contoh untuk nilai eigen dari p-Laplacian pada SM yang melibatkan aliran Ricci pada M .Kata kunci: aliran Ricci, manifold Finsler, operator p-Laplace