IJPAM: Volume 30, No. 4 (2006)

AN EIGENVALUE ESTIMATE FOR MANIFOLDS
WITH PARALLEL RICCI TENSOR

Leung-Fu Cheung$^1$, Pui-Fai Leung$^2$
$^1$Department of Mathematics
Chinese University of Hong Kong
N.T., HONG KONG, P.R. CHINA
e-mail: lfcheung@math.cuhk.edu.hk
$^2$Department of Mathematics
National University of Singapore
Lower Kent Ridge Road
Singapore, 117543, SINGAPORE
e-mail: matfredl@nus.edu.sg


Abstract.We show that the first eigenvalue of a compact $n$-dimensional manifold which is not isometric to a sphere and which has parallel Ricci tensor and sectional curvatures bounded below by a positive constant $\kappa$ is not less than $2n\kappa$.

Received: June 23, 2006

AMS Subject Classification: 53C20

Key Words and Phrases: eigenvalues, parallel Ricci tensor

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 4