Riemannian nilmanifolds attached to Clifford modules

✍ Scribed by Aroldo Kaplan

• Book ID: 104641779
• Publisher: Springer
• Year: 1981
• Tongue: English
• Weight: 353 KB
• Volume: 11
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00147615

✦ Synopsis

To every Clifford module we associate a two-step nilpotent Lie group with a natural left-invariant metric. Their prototypical features were made evident in [3] in connection with their hypo-elliptic sub-Laplacians, and in many ways they constitute a natural generalization of the Heisenberg group.

In this paper we study some of their geometry (curvatures, geodesics) obtaining as a consequence a description of their isometry group. The latter resembles the situation for bi-invariant (resp. left-invariant) metrics on compact (resp. compact simple) Lie groups ([1], [6]) and the isotropy subgroup at the identity can be identified with the automorphism group of a composition of quadratic forms (cf. [7]). 1. NILMANIFOLDS ATTACHED TO CLIFFORD MODULES * Partially supported by an NSF grant.