Sasakian manifold [SEP] named after
Sasakian manifold
In differential geometry, a Sasakian manifold (named after Shigeo Sasaki) is a contact manifold formula_1 equipped with a special kind of Riemannian metric formula_2, called a "Sasakian" metric.
Definition.
A Sasakian metric is defined using the construction of the "Riemannian cone". Given a Riemannian manifold formula_3, its Riemannian cone is the product 
of formula_5 with a half-line formula_6,
equipped with the "cone metric" 
where formula_8 is the parameter in formula_6.
A manifold formula_5
Reeb vector field
In mathematics, the Reeb vector field, named after the French mathematician Georges Reeb, is a notion that appears in various domains of contact geometry including:
- in a contact manifold, given a contact 1-form formula_1, the Reeb vector field satisfies formula_2 ,
- in particular, in the context of Sasakian manifold#The Reeb vector field.