Premium
The second CR Yamabe invariant
Author(s) -
Barbosa Ezequiel,
Lemos Flávio
Publication year - 2017
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.201500297
Subject(s) - mathematics , yamabe flow , invariant (physics) , hermitian matrix , pure mathematics , eigenvalues and eigenvectors , riemannian manifold , conformal map , mathematical analysis , regular polygon , mathematical physics , scalar curvature , geometry , physics , sectional curvature , curvature , quantum mechanics
Let ( M , θ ) be a closed, connected, strictly pseudoconvex CR manifold with dimension 2 n + 1 ≥ 3 . We define the second CR Yamabe invariant in terms of the second eigenvalue of the Yamabe operator and the volume of M over the pseudo‐convex pseudo‐hermitian structures θ ∼ conformal to θ. Then we study when it is attained and classify the CR‐sphere by its second CR Yamabe invariant. This work is motivated by the work of B. Ammann and E. Humbert [1][B. Ammann, 2006] on the Riemannian context.