[引用][C] Tangent sphere bundles satisfying ∇ξτ=0
D Perrone - Journal of Geometry, 1994 - Springer
Journal of Geometry, 1994•Springer
Let (M, o), g, g) be a contact Riemannian manifold and r=~ g, namely the Lie the Lie
derivative of g with respect to r the torsion introduced by Chern-Hamilton [6]. In [10](see also
[9]) we gave a variational characterization of compact contact Riemannian manifolds which
satisfy the condition (*) v~ r= 0 where V is the Levi-Civita connection of g. We refer to [10]
and [9] for the motivation of the study of the condition (*). Classically a large class of contact
metric manifolds is formed by the tangent sphere bundles of Riemannian manifolds. Let (r …
derivative of g with respect to r the torsion introduced by Chern-Hamilton [6]. In [10](see also
[9]) we gave a variational characterization of compact contact Riemannian manifolds which
satisfy the condition (*) v~ r= 0 where V is the Levi-Civita connection of g. We refer to [10]
and [9] for the motivation of the study of the condition (*). Classically a large class of contact
metric manifolds is formed by the tangent sphere bundles of Riemannian manifolds. Let (r …
Let (M, o), g, g) be a contact Riemannian manifold and r=~ g, namely the Lie the Lie derivative of g with respect to r the torsion introduced by Chern-Hamilton [6]. In [10](see also [9]) we gave a variational characterization of compact contact Riemannian manifolds which satisfy the condition (*) v~ r= 0 where V is the Levi-Civita connection of g. We refer to [10] and [9] for the motivation of the study of the condition (*).
Classically a large class of contact metric manifolds is formed by the tangent sphere bundles of Riemannian manifolds. Let (r the standard contact metric structure of the tangent sphere bundle TIN of a R~ emannian manifold (N, G). A well-known result of Tashiro (el. Ill p. 136) states that (TiN, o), g, O is K-contact, namely~---0, if and only if (N, g) has constant
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