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August 14, 2026Journal of Geometric AnalysisOpen Access

Steady Gradient Ricci Solitons with O(p)× O(q) Symmetry

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Construct new examples of steady gradient Ricci solitons with positive curvature operators in dimensions four and higher.
Applied an ansatz and construction procedure introduced by Lai to generate metric solutions.
Imposed $O(p) \times O(q)$ symmetry on $(p + q)$-dimensional spaces for arbitrary integers $p, q \ge 2$.
Established the existence of new steady gradient Ricci solitons possessing positive curvature operators across dimensions $n \ge 4$.
Characterized the asymptotic geometric properties of the newly constructed symmetric solitons.

Implication

Mathematical analysis uncovers new steady gradient Ricci solitons with positive curvature in dimensions four and above, expanding known singularity models in geometric flow.

Abstract

We find new examples of steady gradient Ricci solitons with positive curvature operator in dimensions four and above. Utilising a procedure first introduced by Lai, we construct examples with O(p) × O(q) O ( p ) × O ( q ) symmetry in dimension $$p+q$$ p + q for any pair of integers p,q ≥ 2 p , q ≥ 2 and discuss their asymptotic geometry.

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Cite This Study

Lavoyer et al. (2026) studied this question.

synapsesocial.com/papers/6a7ec69fb70b84ec8b912bbd https://doi.org/10.1007/s12220-026-02567-x

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Implication

Mathematical analysis uncovers new steady gradient Ricci solitons with positive curvature in dimensions four and above, expanding known singularity models in geometric flow.

Steady Gradient Ricci Solitons with O(p)× O(q) Symmetry

Key Points

Implication

Abstract

Discussion

Cite This Study

Steady Gradient Ricci Solitons with O(p)× O(q) Symmetry

Key Points

Implication

Abstract

Discussion

Cite This Study

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