Connected sum construction for $\sigma_k$-Yamabe metrics

Giovanni Catino; Lorenzo Mazzieri

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arXiv · 0910.5353

Connected sum construction for $\sigma_k$-Yamabe metrics

Giovanni Catino·Lorenzo Mazzieri

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Abstract

In this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $\sigma_k$-Yamabe problem, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation.

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Giovanni Catino, Lorenzo Mazzieri. 2009-10-28. Connected sum construction for $\sigma_k$-Yamabe metrics. https://arxiv.org/abs/0910.5353

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