∗-η-Ricci solitons and Einstein metrics on a weak β-Kenmotsu manifold

2025/03/23 by Rovenski, Vladimir
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.18031

Abstract

Weak almost contact metric manifolds (i.e., the complex structure is replaced by a nonsingular skew-symmetric tensor), defined by the author and R. Wolak, allow a new look at the classical theory and find novel applications. An important case of these manifolds, which is locally a twisted product, is a weak β-Kenmotsu manifold defined by the author and D.S. Patra. In the paper, the concept of the ∗-Ricci tensor is adapted to weak almost contact manifolds, the interaction of the ∗-η-Ricci soliton with the weak β-Kenmotsu structure (with β=const) is studied and new characteristics of Einstein metrics are obtained.

Related

• ∗-η-Ricci solitons on weak Kenmotsu f-manifolds
• η-Ricci solitons and η-Einstein metrics on weak β-Kenmotsu f-manifolds
• Almost η-Ricci solitons on Kenmotsu manifolds
• Geometry of almost contact metrics as almost *-Ricci solitons
• Geometry of almost contact metrics as an almost ∗-η-Ricci–Bourguignon solitons