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**Additional info for Algerbaic Geometry and Its Applications: Dedicated to Gilles Lachaud on His 60th Birthday (Series on Number Theory and Its Applications)**

**Example text**

The condition of zero curvature yields that the distinct principal curvatures are at most two and one of principal curvatures with at least n - 1 multiplicities is zero. Furthermore, the scalar curvature is zero. 1). 5 (Cheng [4]). / / Mn is an oriented complete hypersurface in E n + 1 , n > 2, with constant scalar curvature n(n — l)r and with two distinct principal curvatures, then Mn is isometric to one of the following hypersurfaces: (1) E"- f c x Sk(c), forl

Diff. Geom. 32 (1990), 155-183. [N] H. Nakajima, Compactness of the moduli space of Yang-Mills connections in higher dimensions, J. Math. Soc. Japan 4 0 (1988), no. 3, 383-392. [S] S. Sedlacek, A direct method for minimizing the Yang-Mills functional over 4manifolds, Commun. Math. Phys. 86 (1982), 515-527. [U] K. K. Uhlenbeck, Connections with V bounds on curvature, Commun. Math. Phys. 8 3 (1982), 31-42. T H E ESSENTIAL S P E C T R U M ON COMPLETE N O N C O M P A C T RIEMANNIAN MANIFOLDS W I T H ASYMPTOTICALLY N O N N E G A T I V E RADIAL RICCI CURVATURE CHEN ZHIHUA* (Department of Applied Mathematics, Tongji university, Shanghai 200092) ZHUO CHAOHUI** (Department of Information and Computing Science, Shanghai university of Electric Power, Shanghai 200090) ABSTRACT.

P* We want to prove that this case can not be happened. Let q^supl-F^I2, then f < p. <9\ P,(J) S U p p,(w\ Pf(z) | ^ | 2 < z+a ^. 5)