Математика Этерна
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On trans hyperbolic Sasakian manifolds

Pankaj

After finding some basic results on trans hyperbolic Sasakian manifold, we find explicit formulae for Ricci operator, Ricci tensor and curvature tensor in a three-dimensional trans hyperbolic Sasakian manifold. It is also proved that, in a three-dimensional trans hyperbolic Sasakian manifold QÏ• = Ï•Q if gradβ = −Ï•(gradα). Finally we find expression for Ricci tensor in three-dimensional trans hyperbolic Sasakian manifold in case of the manifold being η-Einstein or Ricci semi symmetric.