Mathematica Eterna
Open Access

Abstract

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 Qϕ = ϕQ if gradβ = −ϕ(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.