Induced almost para-Kähler Einstein metrics on cotangent bundles

Fuente: arXiv
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Autori principali: Cap, Andreas, Mettler, Thomas
Natura: Preprint
Pubblicazione: 2023
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author Cap, Andreas
Mettler, Thomas
author_facet Cap, Andreas
Mettler, Thomas
contents In earlier work we have shown that for certain geometric structures on a smooth manifold $M$ of dimension $n$, one obtains an almost para-Kähler--Einstein metric on a manifold $A$ of dimension $2n$ associated to the structure on $M$. The geometry also associates a diffeomorphism between $A$ and $T^*M$ to any torsion-free connection compatible with the geometric structure. Hence we can use this construction to associate to each compatible connection an almost para-Kähler--Einstein metric on $T^*M$. In this short article, we discuss the relation of these metrics to Patterson--Walker metrics and derive explicit formulae for them in the cases of projective, conformal and Grassmannian structures.
format Preprint
id arxiv_https___arxiv_org_abs_2301_03217
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Induced almost para-Kähler Einstein metrics on cotangent bundles
Cap, Andreas
Mettler, Thomas
Differential Geometry
In earlier work we have shown that for certain geometric structures on a smooth manifold $M$ of dimension $n$, one obtains an almost para-Kähler--Einstein metric on a manifold $A$ of dimension $2n$ associated to the structure on $M$. The geometry also associates a diffeomorphism between $A$ and $T^*M$ to any torsion-free connection compatible with the geometric structure. Hence we can use this construction to associate to each compatible connection an almost para-Kähler--Einstein metric on $T^*M$. In this short article, we discuss the relation of these metrics to Patterson--Walker metrics and derive explicit formulae for them in the cases of projective, conformal and Grassmannian structures.
title Induced almost para-Kähler Einstein metrics on cotangent bundles
topic Differential Geometry
url https://arxiv.org/abs/2301.03217