The Ricci flow for simply connected nilmanifolds

The Ricci Flow for Nilmanifolds

We consider the Ricci flow for simply connected nilmanifolds, which translates to a Ricci flow on the space of nilpotent metric Lie algebras. We consider the evolution of the inner product with respect to time and the evolution of structure constants with respect to time, as well as the evolution of these quantities modulo rescaling. We set up systems of O.D.E.’s for some of these flows and des...

Smooth Structures and Normalized Ricci Flows on Non-Simply Connected Four-Manifolds

A solution to the normalized Ricci flow is called non-singular if it exists for all time with uniformly bounded sectional curvature. By using the techniques developed by the present authors [14, 26], we study the existence or non-existence of non-singular solutions of the normalized Ricci flow on 4−manifolds with non-trivial fundamental group and the relation with the smooth structures. For exa...

On 5-dimensional 2-step homogeneous randers nilmanifolds of Douglas type

‎In this paper we first obtain the non-Riemannian Randers metrics of Douglas type on two-step homogeneous nilmanifolds of dimension five‎. ‎Then we explicitly give the flag curvature formulae and the $S$-curvature formulae for the Randers metrics of Douglas type on these spaces‎. ‎Moreover‎, ‎we prove that the only simply connected five-dimensional two-step homogeneous Randers nilmanifolds of D...

Some results of semilocally simply connected property

If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

Ricci Lower Bound for Kähler–ricci Flow