Abstract: First, we prove that a
-space
satisfying where
denotes the cyclic sum over X, Y, Zis
either h-Einstein or Sasakian or
locally isometric up to D-homothetic
deformation, to a unit tangent sphere bundle of some space of constant curvature
Next,
we prove that a
-space
which is isometrically immersed in a Riemannian manifold of constant curvature cis either Sasakian or locally isometric, up to D-homothetic
deformation, to a unit tangent sphere bundle of some space of constant curvature
or
locally isometric to the trivial bundle
Keywords and phrases: contact metric manifolds, tangent sphere bundle,
-space.
