On the Ricci curvature of steady gradient Ricci solitons

Assume ( M n , g ) is a complete steady gradient Ricci soliton with positive Ricci curvature. If the scalar curvature approaches 0 towards infinity, we prove that ∫ 0 + ∞ Rc ( γ ˙ ( s ) , γ ˙ ( s ) ) d s = R ( O ) , where O is the point where R obtains its maximum and γ ( s ) is a minimal normal geodesic emanating from O. Some other results on the Ricci curvature are also obtained.