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Abstract
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We show that the conservation of energy–momentum tensor of a gravitational model
with Einstein–Hilbert like action on a nearly K¨ahler manifold with the scalar curvature
of a curvature-like tensor, is consistent with the nearly K¨ahler properties. In this way, the
nearly K¨ahler structure is automatically manifested in the action as a induced matter
field. As an example of nearly K¨ahler manifold, we consider the group manifold of
R×II ×S3 ×S3 on which we identify a nearly K¨ahler structure and solve the Einstein
equations to interpret the model. It is shown that the nearly K¨ahler structure in this
example is capable of alleviating the well known fine tuning problem of the cosmological
constant. Moreover, this structure may be considered as a potential candidate for dark
energy.
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