By L. Badescu, D. Popescu

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**Additional resources for Algebraic Geometry Bucharest 1982. Proc. conf**

**Sample text**

D. §5. 1 in [CS]). 9) above without the term Ra. Proposition A . l For any e > 0 and any 0 < R < RM, there exists a constant 8 > 0 (6 < | ) depending on e,R and the geometry of M, such that ifO

Therefore, (N, a) > 0 or (JV, a) = 0. 2 holds. In particular, when n = 3, the author and Wan [8] proved that the assertion due to Nomizu and Smyth [26] is true without the assumption on the sectional curvature. 3 (Cheng and Wan [8]). Let Mn be an oriented complete hypersurface in E 4 with constant scalar curvature. If the mean curvature is constant, then Mn is isometric to a standard round sphere, the Euclidean three-space E 3 or the Riemannian product Sk(c) x E 3 _ f c for k = 1,2. In 1982, Yau [34] proposed to study oriented compact hypersurfaces with constant scalar curvature in E™+1 and conjectured the following Yau's conjecture .

Ls Ya{BRl(xn)} -°° ^ sv '^°°