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On vector bundle manifolds with spherically symmetric metrics

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 نشر من قبل Rui Albuquerque
 تاريخ النشر 2014
  مجال البحث
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 تأليف Rui Albuquerque




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We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle $Erightarrow M$, over a Riemannian manifold $M$, when $E$ is endowed with a metric connection. The tangent bundle of $E$ admits a canonical decomposition and thus it is possible to define an interesting class of two-weights metrics with the weight functions depending on the fibre norm of $E$; hence the generalized concept of spherically symmetric metrics. We study its main properties and curvature equations. Finally we focus on a few applications and compute the holonomy of Bryant-Salamon type $mathrm{G}_2$ manifolds.



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