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The Ricci tensor of almost parahermitian manifolds

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 نشر من قبل Diego Conti
 تاريخ النشر 2016
  مجال البحث
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We study the pseudoriemannian geometry of almost parahermitian manifolds, obtaining a formula for the Ricci tensor of the Levi-Civita connection. The formula uses the intrinsic torsion of an underlying SL(n,R)-structure; we express it in terms of exterior derivatives of some appropriately defined differential forms. As an application, we construct Einstein and Ricci-flat examples on Lie groups. We disprove the parakahler version of the Goldberg conjecture, and obtain the first compact examples of a non-flat, Ricci-flat nearly parakahler structure. We study the paracomplex analogue of the first Chern class in complex geometry, which obstructs the existence of Ricci-flat parakahler metrics.



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