Results in Mathematics

, 60:255 | Cite as

Suspending the Cartan Embedding of \({{\mathbb H}P^n}\) Through Spindles and Generators of Homotopy Groups

Article

Abstract

We provide an equivariant suspension of the Cartan embedding of the symmetric space \({S^{4n+3} \to \mathbb {H}P^n \hookrightarrow Sp(n+1)}\) ; this construction furnishes geometric generators of the homotopy group of π4n+6Sp(n + 1). We study the topology and geometry of the image of this generator; in particular we show that it is a spindle, minimal with respect to the biinvariant metric from Sp(n + 1). This spindle also admits a different metric of positive curvature away from the cone singular point.

Mathematics Subject Classification (2010)

53C30 57T20 

Keywords

Cartan embedding homotopy groups 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.IMECC-UNICAMPCampinasBrazil
  2. 2.Departamento de MatemáticaUFPR, Setor de Ciências Exatas, Centro PolitécnicoCuritibaBrazil
  3. 3.Fakultät für MathematikRuhr-Universität BochumBochumGermany

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