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Deformation and rigidity results for the 2 k ‐Ricci tensor and the 2 k ‐Gauss‐Bonnet curvature
Author(s) -
Caúla Tiago,
Lima Levi Lopes,
Santos Newton Luis
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200228
Subject(s) - mathematics , ricci curvature , rigidity (electromagnetism) , riemann curvature tensor , scalar curvature , ricci decomposition , curvature of riemannian manifolds , ricci flow , mathematical analysis , mathematical physics , pure mathematics , einstein , curvature , weyl tensor , sectional curvature , geometry , physics , quantum mechanics
We present several deformation and rigidity results within the classes of closed Riemannian manifolds which either are 2 k ‐Einstein (in the sense that their 2 k ‐Ricci tensor is constant) or have constant 2 k ‐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.