Research profile

Wafaa Batat

Works on Einstein metrics, almost & η-Ricci solitons and stability & uniqueness.

NP-RC-453673

8
topics
3
co-authors
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Einstein metricsAlmost & η-Ricci solitonsStability & uniquenessKähler–Einstein & K-stabilityRotational symmetry & warped productsRicci flowKähler geometryRicci solitons

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Co-authors

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Frequent co-authors of Wafaa Batat Wafaa Batat in the centre and 3 co-authors around them, closer for more joint papers on this site. Batat Stuart James Hall: 2 joint worksSHHall Thomas Murphy: 2 joint worksTMMurphy James Waldron: 1 joint workJWWaldron
Closer to the centre: more joint work here. have also written together
  1. Stuart James Hall

    2 joint workslatest 2021

  2. Thomas Murphy

    2 joint workslatest 2021

  3. James Waldron

    1 joint worklatest 2021

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Papers

Their work in this field since 2016, with the older papers the site recommends. Titles open each paper's page, with its abstract, PDF and HTML versions; Connections shows the papers closest to it. The arXiv listing has the complete record.

2021

math.DGv2arXiv:2102.07168

Rigidity of -type symmetric spaces

Wafaa Batat, Stuart James Hall, Thomas Murphy, James Waldron

We prove that the bi-invariant Einstein metric on is isolated in the moduli space of Einstein metrics, even though it admits infinitesimal deformations. This gives a non-Kähler, non-product example of this phenomenon adding to the famous example of found by Koiso. We apply our methods to derive similar solitonic rigidity results for the Kähler–Einstein metrics on `odd' Grassmannians. We also make explicit a connection between non-integrable deformations and the dynamical instability of metrics under Ricci flow.

Ricci flowEinstein metricsKähler geometryStability & uniquenessKähler–Einstein & K-stability
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2016

math.DGv3arXiv:1607.05766

Destabilising compact warped product Einstein manifolds

Wafaa Batat, Stuart James Hall, Thomas Murphy

The linear stability of warped product Einstein metrics as fixed points of the Ricci flow is investigated. We generalise the results of Gibbons, Hartnoll and Pope and show that in sufficiently low dimensions, all warped product Einstein metrics are unstable. By exploiting the relationship between warped product Einstein metrics, quasi-Einstein metrics and Ricci solitons, we introduce a new destabilising perturbation (the Ricci variation) and show that certain infinite families of warped product Einstein metrics will be unstable in high dimensions.

Ricci flowRicci solitonsEinstein metricsAlmost & η-Ricci solitonsStability & uniquenessRotational symmetry & warped products
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NP-RC-453673 is Wafaa Batat's permanent number in the Ricci flow community on Neckpinch. It stays with them through any change of name or post. More about these numbers.

A window on one part of a person's work: papers here go back to 2016 and cover Ricci flow and its neighbouring flows, with the older work the site recommends, so this page is no measure of anyone's whole output. Being listed is not an endorsement by or of the person. If two people share this name, their work may appear together here. How it is put together.