Kamiyama, Yasuhiko; Tezuka, Michishige On tangent bundles of certain homogeneous spaces. (English) Zbl 1062.57031 Int. J. Pure Appl. Math. 11, No. 3, 329-334 (2004). Let be \(X_n=SO(n)/(SO(n-4)\times SU(2))\) and \(Y_n=SO(n)/(SO(n-4)\times U(2))\), \(n \geq 4\). The authors compute the total Chern class \(c(Y_n)\) of the tangent bundle of \(Y_n\), and then the total Stiefel-Whitney class \(w(X_n)\) and the total Pontrjagin class \(p(X_n)\) of the tangent bundle of \(X_n\). In particular they prove that \(X_n\) is parallelizable if and only if \(n=4\) or \(5\). Reviewer: Luis A. Cordero (Santiago de Compostela) MSC: 57R20 Characteristic classes and numbers in differential topology 57T15 Homology and cohomology of homogeneous spaces of Lie groups Keywords:homogeneous space; characteristic class PDFBibTeX XMLCite \textit{Y. Kamiyama} and \textit{M. Tezuka}, Int. J. Pure Appl. Math. 11, No. 3, 329--334 (2004; Zbl 1062.57031)