A Ricci Nilsoliton Is Nongradient
نویسنده
چکیده
where λ is the soliton constant. In [2], Lauret proves the existence of many left invariant Ricci solitons on nilpotent Lie groups. The first explicit construction of Lauret solitons has been obtained by Baird and Danielo in [4]. In particular they show that the soliton structure on Nil is of nongradient type. Remarkably this is the first example of nongradient Ricci soliton. In [5], it is proved that any left invariant gradient Ricci soliton must have a nontrivial Euclidean de Rham factor. As an application of this result it is shown that any generalized Heisenberg Lie group is a nongradient left invariant Ricci soliton. In [1], Petersen and Wylie study the rigidity of gradient Ricci solitons with symmetry. Recall that a simply connected gradient Ricci soliton is called rigid if it is isometric to N × R where N is an Einstein manifold and f = λ 2 |x| 2
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