关键词: Busemanu function, exhaustion function, Subharmonic function, convex function, end

Abstract: The authors study complete open manifolds whose curvature is non-negative along ray directions. They prove that such manifold has infinite volume. Cheeger-Gromoll's splitting theorem is generallied. They also study topology of such manifolds.

Key words: Busemanu function, exhaustion function, Subharmonic function, convex function, end