In this paper, we extend the work by the first author and Q. Chen [Duke Math. J. 162 (2013), pp. 1149-1169] to classify n-dimensional (n ≥ 5) complete D-flat gradient steady Ricci solitons. More precisely, we prove that any n-dimensional complete noncompact gradient steady Ricci soliton with vanishing D-tensor is either Ricci-flat, or isometric to the Bryant soliton. Furthermore, the proof extends to the shrinking case and the expanding case as well. [ABSTRACT FROM AUTHOR]
This paper provides certain computations with transfer associated with projective bundles of \mathrm {Spin} vector bundles. One aspect is to revise the proof of the main result of [Trans. Amer. Math. Soc.349 (1997), pp. 4385-4399] which says that all fourfold products of the Ray classes are zero in symplectic cobordism. [ABSTRACT FROM AUTHOR]
This erratum concerns Lemma 3.1 in the original paper [Proc. Amer. Math. Soc. 147 (2019), pp. 1657-1669]. The statement of that lemma needs to be slightly changed since the statement of Claim 3.5 must be changed. The proof of the lemma is mostly still kept as the original one with some lines modified. This change does not effect the proof of the main results. [ABSTRACT FROM AUTHOR]
In our paper "On solvable compact Clifford-Klein forms" [Proc. Amer. Math. Soc. 145 (2017), pp. 1819-1832] we have found a small gap in the proof of the main theorem. In this note we show that the result is correct and that the proof goes through after a slight modification. [ABSTRACT FROM AUTHOR]