
doi: 10.1007/bf02857299
In [Tensor, New Ser. 42, No. 1, 42-54 (1985; Zbl 0578.53027)] the reviewer defined the notion of an almost \(r\)-paracontact manifold of P-Sasakian type. In this paper the authors study the geometry of a special case, an exact 2-para Sasakian manifold. Among other interesting results, they show that if the Reeb 1-forms are exact \((\eta_j=df_j)\) and the covariant derivatives of the Reeb vectors are proportional to the horizontal component of the soldering forms \((\nabla\xi _j=-f_j(dp)^h)\), then the given para-Sasakian manifold \(M\) is locally a Riemannian product \(M^v\times M^h\), where \(M^v\) is a flat surface tangent to \(\xi_j\), while \(M^h\) is a pseudo-umbilical submanifold of \(M\).
exact 2-para Sasakian manifold, Special Riemannian manifolds (Einstein, Sasakian, etc.), Riemannian product, almost \(r\)-paracontact manifold, Reeb 1-forms
exact 2-para Sasakian manifold, Special Riemannian manifolds (Einstein, Sasakian, etc.), Riemannian product, almost \(r\)-paracontact manifold, Reeb 1-forms
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