Abstract
We prove that if a vector field V on a contact metric manifold \({M(\varphi, \xi, \eta, g)}\) of dimension (2n+1) leaves the tensor field \({\varphi}\) invariant, then V is an infinitesimal harmonic transformation. Next, we study contact metric manifolds admitting a vector field V that leaves the structure tensor \({\varphi}\) invariant and satisfies different conditions, namely (1) \({Q\varphi = \varphi Q}\), (2) M is Jacobi \({(k, \mu)}\)-contact manifold, (3) \({R(X, Y)\xi = 0}\), for any vector fields X, Y orthogonal to \({\xi}\) and (4) \({\pounds_{V}C = 0}\), where C is the conformal curvature tensor.
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Ghosh, A. Certain infinitesimal transformations on contact metric manifolds. J. Geom. 106, 137–152 (2015). https://doi.org/10.1007/s00022-014-0240-4
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DOI: https://doi.org/10.1007/s00022-014-0240-4