Geodesics of fiberwise cigar soliton deformation of the Sasaki metric

Abstract

Ricci solitons arose in proof the Poincare conjecture by R. Hamilton and G. Perelman. The first example of a noncompact steady Ricci soliton on a plane was found by R. Hamilton. This two-dimensional manifold is conformally equivalent to the plane and it is called by R. Hamilton's cigar soliton. The cigar soliton metric can be considered as a fiber-wise conformal deformation of the Euclidean metric on a fiber of the tangent bundle. In the paper we propose a deformation of the classical Sasaki metric on the tangent bundle of an n-dimensional Riemannian manifold that induces the cigar soliton type metric on the fibers. The purpose of the research is to study geodesics of the cigar soliton deformation of the Sasaki metric on the tangent bundle of the Riemannian manifold with focus on the locally symmetric/constant curvature base manifold.