Bochner flatness of tangent bundles with g-natural almost Hermitian metrics


Blair D. E. , Yildirim H.

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, vol.49, no.3, pp.259-269, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 3
  • Publication Date: 2016
  • Doi Number: 10.1007/s10455-015-9491-z
  • Journal Name: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.259-269

Abstract

We consider g-natural metrics on the tangent bundle of a Riemannian manifold together with the almost complex structure which reverses the horizontal and vertical subspaces. This narrows the class of g-natural metrics to metrics conformally equivalent to the Sasaki metric on the tangent bundle with a restriction on the conformal factor. We then show that such a g-natural almost Hermitian structure is Bochner flat if and only if it is conformally equivalent to the Sasaki metric when the base manifold is flat and with the same restriction on the conformal factor.