Kodai Mathematical Journal

On hypersurfaces into Riemannian spaces of constant sectional curvature

Antonio Caminha

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.

Article information

Source
Kodai Math. J., Volume 29, Number 2 (2006), 185-210.

Dates
First available in Project Euclid: 3 July 2006

https://projecteuclid.org/euclid.kmj/1151936435

Digital Object Identifier
doi:10.2996/kmj/1151936435

Mathematical Reviews number (MathSciNet)
MR2247430

Zentralblatt MATH identifier
1107.53037

Citation

Caminha, Antonio. On hypersurfaces into Riemannian spaces of constant sectional curvature. Kodai Math. J. 29 (2006), no. 2, 185--210. doi:10.2996/kmj/1151936435. https://projecteuclid.org/euclid.kmj/1151936435