On metrics of positive Ricci curvature conformal to $M\times {𝐑}^m$

Ruiz, Juan Miguel. "On metrics of positive Ricci curvature conformal to $M\times \mathbf {R}^m$." Archivum Mathematicum 045.2 (2009): 105-113. <http://eudml.org/doc/250676>.

@article{Ruiz2009,
abstract = {Let $(M^n,g)$ be a closed Riemannian manifold and $g_E$ the Euclidean metric. We show that for $m>1$, $\left(M^n \times \mathbf \{R\}^m, (g+g_E)\right)$ is not conformal to a positive Einstein manifold. Moreover, $\left(M^n \times \mathbf \{R\}^m, (g+g_E)\right)$ is not conformal to a Riemannian manifold of positive Ricci curvature, through a radial, integrable, smooth function, $\varphi \colon \mathbf \{R^m\} \rightarrow \mathbf \{R^+\}$, for $m>1$. These results are motivated by some recent questions on Yamabe constants.},
author = {Ruiz, Juan Miguel},
journal = {Archivum Mathematicum},
keywords = {conformally Einstein manifolds; positive Ricci curvature; conformally Einstein manifold; positive Ricci curvature},
language = {eng},
number = {2},
pages = {105-113},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On metrics of positive Ricci curvature conformal to $M\times \mathbf \{R\}^m$},
url = {http://eudml.org/doc/250676},
volume = {045},
year = {2009},
}

TY - JOUR
AU - Ruiz, Juan Miguel
TI - On metrics of positive Ricci curvature conformal to $M\times \mathbf {R}^m$
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 2
SP - 105
EP - 113
AB - Let $(M^n,g)$ be a closed Riemannian manifold and $g_E$ the Euclidean metric. We show that for $m>1$, $\left(M^n \times \mathbf {R}^m, (g+g_E)\right)$ is not conformal to a positive Einstein manifold. Moreover, $\left(M^n \times \mathbf {R}^m, (g+g_E)\right)$ is not conformal to a Riemannian manifold of positive Ricci curvature, through a radial, integrable, smooth function, $\varphi \colon \mathbf {R^m} \rightarrow \mathbf {R^+}$, for $m>1$. These results are motivated by some recent questions on Yamabe constants.
LA - eng
KW - conformally Einstein manifolds; positive Ricci curvature; conformally Einstein manifold; positive Ricci curvature
UR - http://eudml.org/doc/250676
ER -