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CHARACTERIZATION OF 3-DIMENSIONAL NORMAL ALMOST CONTACT METRIC MANIFOLDS ADMITTING NEARLY VACUUM STATIC EQUATIONS
Keywords:
normal almost contact metric manifolds, nearly vacuum static equation, scalar curvature, Einstein manifolds, rigidity, contact geometryDOI:
https://doi.org/10.17654/0972415X25010Abstract
This paper investigates nearly vacuum static equations (NVSE) on 3‑dimensional normal almost contact metric manifolds. We derive structural constraints imposed by the existence of smooth solutions to the NVSE, particularly examining the conditions under which scalar curvature becomes constant or the manifold admits Einstein-type metrics. A key result establishes that if the gradient of the potential function is nowhere vanishing, then the scalar curvature must be constant and the manifold either Einstein or of constant sectional curvature. An explicit example of a flat cosymplectic manifold admitting a non-trivial solution to the NVSE is also constructed to illustrate the sharpness of the derived results.
Received: September 9, 2025
Accepted: October 18, 2025
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