Four-dimensional Einstein metrics from biconformal deformations

Paul Baird; Jade Ventura

Archivum Mathematicum (2021)

  • Volume: 057, Issue: 5, page 255-283
  • ISSN: 0044-8753

Abstract

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Biconformal deformations take place in the presence of a conformal foliation, deforming by different factors tangent to and orthogonal to the foliation. Four-manifolds endowed with a conformal foliation by surfaces present a natural context to put into effect this process. We develop the tools to calculate the transformation of the Ricci curvature under such deformations and apply our method to construct Einstein 4 -manifolds. Examples of one particular family have ends which collapse asymptotically to ℝ 2 .

How to cite

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Baird, Paul, and Ventura, Jade. "Four-dimensional Einstein metrics from biconformal deformations." Archivum Mathematicum 057.5 (2021): 255-283. <http://eudml.org/doc/297881>.

@article{Baird2021,
abstract = {Biconformal deformations take place in the presence of a conformal foliation, deforming by different factors tangent to and orthogonal to the foliation. Four-manifolds endowed with a conformal foliation by surfaces present a natural context to put into effect this process. We develop the tools to calculate the transformation of the Ricci curvature under such deformations and apply our method to construct Einstein $4$-manifolds. Examples of one particular family have ends which collapse asymptotically to $\mathbb \{R\}^2$.},
author = {Baird, Paul, Ventura, Jade},
journal = {Archivum Mathematicum},
keywords = {Einstein manifold; conformal foliation; semi-conformal map; biconformal deformation},
language = {eng},
number = {5},
pages = {255-283},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Four-dimensional Einstein metrics from biconformal deformations},
url = {http://eudml.org/doc/297881},
volume = {057},
year = {2021},
}

TY - JOUR
AU - Baird, Paul
AU - Ventura, Jade
TI - Four-dimensional Einstein metrics from biconformal deformations
JO - Archivum Mathematicum
PY - 2021
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 057
IS - 5
SP - 255
EP - 283
AB - Biconformal deformations take place in the presence of a conformal foliation, deforming by different factors tangent to and orthogonal to the foliation. Four-manifolds endowed with a conformal foliation by surfaces present a natural context to put into effect this process. We develop the tools to calculate the transformation of the Ricci curvature under such deformations and apply our method to construct Einstein $4$-manifolds. Examples of one particular family have ends which collapse asymptotically to $\mathbb {R}^2$.
LA - eng
KW - Einstein manifold; conformal foliation; semi-conformal map; biconformal deformation
UR - http://eudml.org/doc/297881
ER -

References

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  10. Schoen, R., 10.4310/jdg/1214439291, J. Differential Geom. 20 (1984), 479–495. (1984) Zbl0576.53028DOI10.4310/jdg/1214439291
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