Summary
The Lie groups G2 and Spin(7) can be considered as automorphisms groups of euclidean vector spaces (of dimension 7, 8 resp.) endowed with a suitable vector product (cfr. [12]). Here one put in evidence several geometric properties of certain special subspaces of such euclidean spaces and the manifolds of special subspaces are determined as well known homogeneous spaces. One considers also riemannian manifolds with holonomy group G2 or Spin(7) establishing that in the analytic case the existence of a totally geodesic submanifold of codimension 1 imply local reducibility.
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Lavoro svolto nell'ambito del «Gruppo Nazionale Structure Algebriche, Geometriche e Applicazioni (Consiglio Nazionale delle Ricerche)».
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Marchiafava, S. Alcune osservazioni riguardanti i gruppi di LieG 2 e Spin(7), candidati a gruppi di olonomia. Annali di Matematica pura ed applicata 129, 247–264 (1981). https://doi.org/10.1007/BF01762145
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DOI: https://doi.org/10.1007/BF01762145