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D-conharmonic change in a special para-Sasakian manifold. (English) Zbl 0746.53036
Let \(M\) be an \(n\)-dimensional manifold with two para-Sasakian structures \(S=(\varphi,\xi,\eta,g)\) and \(^*S=(^*\varphi,^*\xi,^*\eta,^*g)\) satisfying: (*) \(^*g_{ij}=e^{2k}g_{ij}+(e^{2r}-e^{2k})\eta_ i\eta_ j\), \(^*\xi^ i=e^{-r}\xi^ i\), \(^*\varphi^ i_ j=\varepsilon\cdot\varphi^ i_ j\), \(^*\eta_ i=\varepsilon e^ r\eta_ i\), \(\varepsilon=\pm1\), where \(k\) and \(r\) are functions on \(M\). Then, \(S\) and \(^*S\) have the same \(D\)-distributions, i.e. \((n-1)\)- dimensional distributions \(D\) and \(^*D\) defined by \(\eta=0\) and \(^*\eta=0\), respectively. The relation (*) is said to be a \(D\)- conformal change of \(S\). In this paper, the author introduces the notion of a \(D\)-conharmonic change (special case of \(D\)-conformal change) in a special para-Sasakian manifold, and obtains the \(D\)-conharmonic curvature tensor field, i.e. the tensor that is invariant under a \(D\)-conharmonic change. Moreover, a number of interesting properties of this change has been studied.
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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