In this paper, we discuss the lower diameter estimate for a class of compact generalized quasi-Einstein manifolds which are closely related to the conformal geometry. Using the Bochner formula and the Hopf maximum principle, we get a gradient estimate for the potential function of the manifold. Based on the gradient estimate, we get the lower diameter estimate for this class of generalized quasi-Einstein manifolds.
"Diameter estimate for a class of compact generalized quasi-Einstein manifolds,"
Turkish Journal of Mathematics: Vol. 45:
5, Article 31.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss5/31