Some Eigenvalues Estimate for the ϕ-Laplace Operator on Slant Submanifolds of Sasakian Space Forms. (13th October 2021) - Li, Yanlin; Ali, Akram; Mofarreh, Fatemah; Abolarinwa, Abimbola; Ali, Rifaqat
Abstract : This paper is aimed at establishing new upper bounds for the first positive eigenvalue of the ϕ -Laplacian operator on Riemannian manifolds in terms of mean curvature and constant sectional curvature. The first eigenvalue for the ϕ -Laplacian operator on closed oriented m -dimensional slant submanifolds in a Sasakian space form M ~ 2 k + 1 ε is estimated in various ways. Several Reilly-like inequalities are generalized from our findings for Laplacian to the ϕ -Laplacian on slant submanifold in a sphere S 2 n + 1 with ε = 1 and ϕ = 2 .