*-Miao-Tam equation on contact geometry

Uday Chand De, Shahroud Azami

Abstract


In this article, we classify *-Miao-Tam equations in contact geometry. In the beginning, it is demonstrated that if a Sasakian manifold satisfies *-Miao-Tam equation with the potential function $\lambda$, then $\lambda = c_1 t +c_2,\,\, c_1\neq 0$, provided the scalar curvature is invariant under $\zeta$. Also, we show that if a Sasakian 3-manifold satisfies *-Miao-Tam equation with non-constant potential function, then the manifold is *-Ricci flat and becomes a Sasakian space-form. Next, we characterize *-Miao-Tam equation on $(k,\mu)$-contact manifolds.

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References


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DOI: https://doi.org/10.52846/ami.v52i2.1881