Work

Computationally assisted proof of a novel O(3)×O(10)‐invariant Einstein metric on S12

Year: 2026

Type: article

Abstract: We prove the existence of a non‐round Einstein metric on that is invariant under the usual cohomogeneity one action of on . The proof involves using several rigorous numerical analysis techniques to produce a Riemannian metric which approximately satisfies the Einstein condition to known high precision, and then demonstrating that can be perturbed into a true Einstein metric .

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70477

Authors: Timothy Buttsworth, Liam Hodgkinson

Institutions: UNSW Sydney, The University of Melbourne

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: bronze

Funder: Australian Research Council

Awards: Distinguished Geometric Structures with Symmetry in Four Dimensions, Universal Model Selection Criteria for Scientific Machine Learning