Deformation and rigidity results for the 2k-Ricci tensor and the 2k-Gauss-Bonnet curvature

作者：Caula Tiago; de Lima Levi Lopes^*; Santos Newton Luis

来源：Mathematische Nachrichten, 2013, 286(17-18): 1752-1777.

DOI：10.1002/mana.201200228

• 2k-Ricci tensor
• 2k-Gauss-Bonnet curvature
• deformation
• rigidity
• double forms
• Yamabe problem

We present several deformation and rigidity results within the classes of closed Riemannian manifolds which either are 2k-Einstein (in the sense that their 2k-Ricci tensor is constant) or have constant 2k-Gauss-Bonnet curvature. The results hold for a family of manifolds containing all non-flat space forms and the main ingredients in the proofs are explicit formulae for the linearizations of the above invariants obtained by means of the formalism of double forms.

• 出版日期2013-12