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- Title
ALMOST η-RICCI SOLITONS ON TWO CLASSES OF ALMOST KENMOTSU MANIFOLDS.
- Authors
DEY, Dibakar; MAJHI, Pradip
- Abstract
The object of the present paper is to characterize two classes of almost Kenmotsu manifolds admitting almost η-Ricci solitons. In this context we have shown that in a (k, μ) and (k, μ)′-almost Kenmotsu manifold admitting an almost η-Ricci soliton the curvature conditions (i) the manifold is Einstein, (ii) the manifold is Ricci symmetric (∇S = 0), (iii) the manifold is Ricci semisymmetric (R · S = 0) and (iv) the manifold is projective Ricci semisymmetric (P · S = 0) are equivalent. Also we have shown that the curvature condition Q · P = 0 in a (k, μ)-almost Kenmotsu manifold admitting an almost η-Ricci soliton holds if and only if the manifold is locally isometric to the hyperbolic space H2n+1(-1) and if a (k, μ)′-almost Kenmotsu manifold admitting an almost η-Ricci soliton satisfies the curvature condition Q · R = 0, then it is locally isometric to the Riemannian product Hn+1(-4) × Rn.
- Subjects
EINSTEIN, Albert, 1879-1955; EINSTEIN manifolds; SOLITONS; HYPERBOLIC spaces; CURVATURE
- Publication
Bulletin of the Transilvania University of Braşov: Series III Mathematics & Computer Science, 2024, Vol 66, Issue 1, p35
- ISSN
2810-2029
- Publication type
Article
- DOI
10.31926/but.mif.2024.4.66.1.3