We show that the only shrinking gradient solitons with vanishing Weyl tensor are quotients of the standard ones Sn; Sn 1 R; and Rn. This gives a new proof of the Hamilton-Ivey-PerelÂ’man classiÂ…cationâ€¦ (More)

The question of when an Einstein metric can be written as a warped product is posed in the text Einstein metrics by Besse. Recently, there have been some interesting results about these spaces foundâ€¦ (More)

We prove a new generalization of the Cheeger-Gromoll splitting theorem where we obtain a warped product splitting under the existence of a line. The curvature condition in our splitting is aâ€¦ (More)

We define a gradient Ricci soliton to be rigid if it is a flat bundle NÃ—Î“R k where N is Einstein. It is known that not all gradient solitons are rigid. Here we offer several natural conditions on theâ€¦ (More)

We study gradient Ricci solitons with maximal symmetry. First we show that there are no nontrivial homogeneous gradient Ricci solitons. Thus, the most symmetry one can expect is an isometricâ€¦ (More)

We prove that complete warped product Einstein metrics with isometric bases, simply connected space form fibers, and the same Ricci curvature and dimension are isometric. In the compact case we alsoâ€¦ (More)

In this paper we introduce a vector space of virtual warping functions that yield Einstein metrics over a fixed base. There is a natural quadratic form on this space and we study how this formâ€¦ (More)

In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then theâ€¦ (More)

This paper describes the validation of a molecular docking method and its application to virtual database screening. The code flexibly docks ligand molecules into rigid receptor structures using aâ€¦ (More)

The dominance of the major transcript isoform relative to other isoforms from the same gene generated by alternative splicing (AS) is essential to the maintenance of normal cellular physiology.â€¦ (More)