Second Yamabe constant on Riemannian products
نویسنده
چکیده
Let (M, g) be a closed Riemannian manifold (m ≥ 2) of positive scalar curvature and (N, h) any closed manifold. We study the asymptotic behaviour of the second Yamabe constant and the second N−Yamabe constant of (M × N, g + th) as t goes to +∞. We obtain that limt→+∞ Y (M ×N, [g+ th]) = 2 2 m+n Y (M ×R, [g+ ge]). If n ≥ 2, we show the existence of nodal solutions of the Yamabe equation on (M × N, g + th) (provided t large enough). When sg is constant, we prove that limt→+∞ Y 2 N(M × N, g + th) = 2 2 m+n YRn(M × R , g + ge). Also we study the second Yamabe invariant and the second N−Yamabe invariant.
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