Abstract
In this paper, we compute Lr (Sr) for an isometric immersion x : Mn → $\overline M^{n+1}_c$, from an n-dimensional Riemannian manifold Mn into an (n+1)-dimensional Riemannian manifold $\overline M^{n+1}_c$, of constant sectional curvature c. Here, by Lr we mean the linearization of the second order differential operator associated to the (r+1)-th elementary symmetric function Sr+1 on the eigenvalues of the second fundamental form A of x. The resulting formulae are then applied to study how the behavior of higher-order mean curvature functions of Mn influence its geometry.
Citation
Antonio Caminha. "On hypersurfaces into Riemannian spaces of constant sectional curvature." Kodai Math. J. 29 (2) 185 - 210, June 2006. https://doi.org/10.2996/kmj/1151936435
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