The First Eigenvalue of $(p, q)$-Laplacian System on $C$-Totally Real Submanifold in Sasakian Manifolds

Abstract

Consider $(M, g)$ as an $n$-dimensional compact Riemannian manifold. Our main aim in this paper is to study the first eigenvalue of $(p, q)$-Laplacian system on $C$-totally real submanifold in Sasakian space of form $\overline{M}^{2m+1} (\kappa).$ Also in the case of $p, q > n$ we show that for $λ_{1,p,q}$ arbitrary large there exists a Riemannian metric of volume one conformal to the standard metric of $S^n.$