Almost $$\eta $$-Ricci solitons on Kenmotsu manifolds

Notes on η‐Einstein solitons on para‐Kenmotsu manifolds

“…where S represents the Ricci tensor of E, Q is the Ricci operator defined by S( 1 ,  4 ) = g(Q 1 ,  4 ), and R represents the Riemann curvature tensor of E [4,7].…”

“…Over the past few years, Ricci and Yamabe solitons have attracted the attention and interest of many geometers. We refer [2][3][4][5][6][7][8][9][10].…”

Contractibility of homogeneous Kenmotsu manifolds

“…η-Einstein manifolds, almost η-Ricci solitons) and the differential geometry of relevant kind of submanifolds (e.g. like warped product submanifolds); see for instance [4,8,10,13]. The interested reader can find a discussion of recent results about Kenmotsu manifolds in [1, Section 2], including a rich bibliography on the subject.…”

Back to Almost Ricci Solitons

“…In [15], almost Ricci complete gradient solitons are considered. Other more recent papers have studied compact almost Ricci solitons (e.g., [3,2,8]) or almost Ricci solitons on manifolds with additional geometric structures, e.g., [10,14]. There are also attempts to find applications of almost Ricci solitons in theoretical physics, see, e.g., [9].…”