The critical point equation on Kenmotsu and almost Kenmotsu manifolds
Copyright policy )The critical point equation on Kenmotsu and almost Kenmotsu manifolds
In this paper, we have studied the critical point equation (shortly, CPE) within the frame-work of Kenmotsu and almost Kenmotsu manifold satisfying certain nullity conditions. First, we prove that a complete Kenmotsu metric satisfies the CPE is Einstein and locally isometric to the hyperbolic space H2n+1. In case of Kenmotsu manifolds, it is possible to determine the potential function explicitly (locally). We also provide some examples of Kenmotsu and almost Kenmotsu manifolds that satisfies the CPE.
arXiv admin note: text overlap with arXiv:1701.04996
Mathematics - Differential Geometry, Differential Geometry (math.DG), 53D15, 53C25, 53C21, FOS: Mathematics
Mathematics - Differential Geometry, Differential Geometry (math.DG), 53D15, 53C25, 53C21, FOS: Mathematics
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