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• W2887309039 abstract "For a closed, connected direct product Riemannian manifold $(M, g)=(M_1timescdotstimes M_l, g_1opluscdotsoplus g_l)$, we define its multiconformal class $ [![ g ]!]$ as the totality ${f_1^2g_1oplus cdotsoplus f_l^2g_l}$ of all Riemannian metrics obtained from multiplying the metric $g_i$ of each factor $M_i$ by a function $f_i^2>0$ on the total space $M$. A multiconformal class $ [![ g ]!]$ contains not only all warped product type deformations of $g$ but also the whole conformal class $[tilde{g}]$ of every $tilde{g}in [![ g ]!]$. In this article, we prove that $ [![ g ]!]$ carries a metric of positive scalar curvature if and only if the conformal class of some factor $(M_i, g_i)$ does, under the technical assumption $dim M_ige 2$. We also show that, even in the case where every factor $(M_i, g_i)$ has positive scalar curvature, $ [![ g ]!]$ carries a metric of scalar curvature constantly equal to $-1$ and with arbitrarily large volume, provided $lge 2$ and $dim Mge 3$. In this case, such negative scalar curvature metrics within $ [![ g ]!]$ for $l=2$ cannot be of any warped product type." @default.
• W2887309039 created "2018-08-22" @default.
• W2887309039 creator A5031898734 @default.
• W2887309039 creator A5084348461 @default.
• W2887309039 date "2018-08-20" @default.
• W2887309039 modified "2023-09-27" @default.
• W2887309039 title "Scalar curvature and the multiconformal class of a direct product Riemannian manifold" @default.
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• W2887309039 hasPublicationYear "2018" @default.
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