Complete Riemannian metrics with holonomy group \(G_2\) on deformations of cones over \(S^3\times S^3\)

DOI10.1134/S0001434613050015zbMath1281.53052arXiv1301.6379OpenAlexW2025593529WikidataQ115253930 ScholiaQ115253930MaRDI QIDQ358155

Yaroslav V. Bazaikin, Olga Anatolevna Bogoyavlenskaya

Publication date: 16 August 2013

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.6379

zbMATH Keywords

Riemannian metricKilling vector fieldvector bundleholonomy group \(G_2\)metric on cones over \(S^3\times S^3\)

Mathematics Subject Classification ID

Issues of holonomy in differential geometry (53C29)

Related Items (7)

Invariant torsion and \(\mathrm{G}_2\)-metrics ⋮ \(S^1\)-quotient of \(\mathrm{Spin}(7)\)-structures ⋮ $$\mathrm{G}_2$$-Instantons on Noncompact $$\mathrm{G}_2$$-Manifolds: Results and Open Problems ⋮ \(\operatorname{SU}(2)^2\)-invariant \(G_2\)-instantons ⋮ Infinitely many new families of complete cohomogeneity one \(G_2\)-manifolds: \(G_2\) analogues of the Taub-NUT and Eguchi-Hanson spaces ⋮ A new incomplete Ricci-flat metric ⋮ A geometric flow in the space of \(G^2\)-structures on the cone over \(S^3\times S^3\)

Cites Work

• On new explicit Riemannian \(SU(2(n + 1))\)-holonomy metrics
• Noncompact Riemannian spaces with the holonomy group spin\((7)\) and 3-Sasakian manifolds
• Einstein metrics on \(S^ 3\), \(R^ 3\) and \(R^ 4\) bundles
• A \(G_2\) unification of the deformed and resolved conifolds
• General metrics of \(G_2\) holonomy and contraction limits
• On the construction of some complete metrics with exceptional holonomy
• Orientifolds and slumps in \(G_{2}\) and \(\text{Spin}(7)\) metrics
• On the new examples of complete noncompact Spin(7)-holonomy metrics
• Gauge theory at large \(N\) and new \(G_2\) holonomy metrics
• \(G_2\) holonomy spaces from invariant three-forms

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