On phi-Recurrent Contact Metric Manifolds
E. Peyghan, H. Nasrabadi, A. Tayebi
TL;DR
This paper proves that 3-dimensional ?-recurrent N(k)-contact metric manifolds are flat and classifies ?-recurrent contact metric manifolds of constant curvature, showing the non-existence of certain non-symmetric cases.
Contribution
It establishes a characterization of 3D ?-recurrent N(k)-contact metric manifolds as flat and classifies ?-recurrent contact metric manifolds with constant curvature, clarifying their geometric structure.
Findings
3D ?-recurrent N(k)-contact metric manifolds are flat
Classification of ?-recurrent contact metric manifolds with constant curvature
No ?-recurrent N(k)-contact metric manifold exists that is neither symmetric nor locally ?-symmetric
Abstract
In this paper, we prove that evry 3-dimensional manifold M is a ?- recurrent N(k)-contact metric manifold if and only if it is flat. Then we classify the ?-recurrent contact metric manifolds of constant curvature. This implies that there exists no ?-recurrent N(k)-contact metric manifold, which is neither symmetric nor locally ?-symmetric.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds