Conformal Killing forms on 2-step nilpotent Riemannian Lie groups
The paper under review contains a study of conformal Killing forms with respect to left-invariant Riemannian metrics on 2-step nilpotent Lie groups \(G\). Thus, one proves that if \(Z\) is the center of \(G\) and \(\dim Z\ge 4\), then every conformal Killing form of degree 2 or 3 is co-closed. If \(\dim Z\le3\), one finds that there exist conformal Killing forms of degree 2 or 3 which are not co-closed only in the following cases: If \(\dim Z=1\) (hence the 2-step nilpotent Lie group \(G\) is necessarily a Heisenberg group) then the left-invariant metric can be arbitrary. If \(\dim Z=2\), then \(G\) must be the direct product of a Heisenberg group with the real line, and the left-invariant metric can be arbitrary again. Finally, if \(\dim Z=3\), then \(G\) is the free 2-step nilpotent Lie group with \(\dim G=6\), and the left-invariant metric belongs to a certain family of metrics parametrized by the positive real numbers.
scientific article; zbMATH DE number 7502422
scientific article