Purpose Cotton soliton is a newly introduced notion in the field of Riemannian manifolds. The object this article to study properties on certain contact metric Design/methodology/approach authors consider almost Kenmotsu 3-manifolds. use local basis manifold that helps terms partial differential equations. Findings First potential vector pointwise collinear with Reeb and prove non-existence suc...

In this paper we consider 4-dimensional steady soliton singularity models, i.e., complete gradient Ricci solitons that arise as the rescaled limit of a finite time singular solution flow on closed 4-manifold. particular, study geometry at infinity such under assumption their tangent is product R with 3-dimensional spherical space form. We also classify flows models in general.

In this paper, we study harmonic and caloric functions of polynomial growth on a complete non-compact gradient shrinking Ricci soliton. On one hand, when the scalar curvature satisfies at least quadratic decay, prove that space with fixed degree is finite dimensional. We also analogous results for ancient functions. other without any condition, sharp dimensional estimates Schrödinger degree.

We consider the Yamabe flow of a conformally Euclidean manifold for which the conformal factor’s reciprocal is a quadratic function of the Cartesian coordinates at each instant in time. This leads to a class of explicit solutions having no continuous symmetries (no Killing fields) but which converge in time to the cigar soliton (in two-dimensions, where the Ricci and Yamabe flows coincide) or i...

The object of the present paper is to consider f-Kenmotsu 3-manifolds
 fulfilling certain curvature conditions on Q-curvature tensor with
 Schouten-van Kampen connection. Certain consequences Q-curvature
 such manifolds bearing Ricci soliton in perspective Schouten-van
 association are likewise displayed. In last segment, examples are
 given.

In this paper we introduce notion of Ricci solitons in -para Kenmotsu manifold with semi -symmetric metric connection. We have found the relations between curvature tensor, tensors and scalar semi-symmetic connection.We proved that 3-dimensional connection is an -Einstein soliton defined on named expanding steady respect to value constant.It Conharmonically flat semi-symmetric manifold.

§0 Introduction. In this paper, we shall give a geometric account of the linear trace Li-Yau-Hamilton (which will be abbreviated as LYH) inequality for the Kähler-Ricci flow proved by LuenFai Tam and the author in [NT1]. To put the result, especially the Liouville theorem for the plurisubharmonic functions, into the right perspective we would also describe some dualities existed in both linear ...