Feng, Huitao; Xu, Guangbo; Zhang, Weiping Real embeddings, \(\eta\)-invariant and Chern-Simons current. (English) Zbl 1185.58009 Pure Appl. Math. Q. 5, No. 3, 1113-1137 (2009). The paper under review is a continuation of a remarkable paper by W. Zhang [Chin. Ann. Math., Ser. B 26, No. 1, 45–56 (2005; Zbl 1078.58012)], where the author has given a geometric proof of the Bismut-Zhang formula. In this paper, the authors apply the method given in the above paper to manifolds embedded in sufficiently high dimensional odd spheres \(S^{2N-1}\). They also establish a Riemann-Roch-type formula for the considered Chern-Simons currents. Reviewer: Witold Mozgawa (Lublin) Cited in 4 Documents MSC: 58J28 Eta-invariants, Chern-Simons invariants Keywords:direct image; Chern-Simmons current; \(\eta\)-invariant; Riemann-Roch; Bismut-Zhang localization formula; \(H\)-quantity Citations:Zbl 1078.58012 PDFBibTeX XMLCite \textit{H. Feng} et al., Pure Appl. Math. Q. 5, No. 3, 1113--1137 (2009; Zbl 1185.58009) Full Text: DOI arXiv