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In this paper, we obtain a Lichnerowicz-type formula for Formula: see text-Witten deformation and give the proof of the Kastler–Kalau–Walze-type theorems associated with Formula: see text-Witten deformation on four-dimensional and six-dimensional almost product Riemannian manifold with (respectively, without) boundary. We give an explanation of the Einstein–Hilbert action for Formula: see text-Witten deformation on four-dimensional manifold with boundary.
Liu et al. (Sat,) studied this question.