The Sasakian Geometry of the Heisenberg Group

Details The Sasakian Geometry of the Heisenberg Group The Sasakian Geometry of the Heisenberg Group

2009-04-08

arxiv.org/abs/0904.1406v1

Bull. Math. Soc. Sci. Math. Roumanie 52 (3), 2009, 251-262

Mathematics

Differential Geometry

12 pages

Scientific paper

In this note I study the Sasakian geometry associated to the standard CR structure on the Heisenberg group, and prove that the Sasaki cone coincides with the set of extremal Sasakian structures. Moreover, the scalar curvature of these extremal metrics is constant if and only if the metric has $\Phi$-sectional curvature $-3.$ I also briefly discuss some relations with the well-know sub-Riemannian geometry of the Heisenberg group as well as the standard Sasakian structure induced on compact quotients.

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