3 problems

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Conjecture that the conformal holonomy is exactly $G_2$ for the non-conformally Einstein example
Consider the conformal class $[g_F]$ defined by the metric in equation, arising from the defining function … where $a_i$ , $i=0,1,\ldots,6$ , and $b$ are real constants. Let $H$ deno…
Conjectureopenconformal-geometry exceptional-holonomy holonomyarXiv posted 2 days ago
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The smooth Cayley fibration non-existence conjecture for full-holonomy Spin(7)-manifolds
A torsion-free ${\mathrm{Spin}}(7)$ -manifold is a Riemannian manifold with torsion-free ${\mathrm{Spin}}(7)$ -structure, and a smooth Cayley fibration is a smooth fibration whose fi…
Conjectureopencalibrated-geometry exceptional-holonomy spin-7-geometryarXiv posted 2 days ago
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The existence conjecture for Ricci-flat Spin(7) metrics on generalized connected sums
Ricci-flat Spin(7) metric conjecture. There exists a Ricci-flat metric of holonomy $\operatorname{Spin}(7)$ on such manifolds.
Conjectureopenexceptional-holonomy ricci-flat-metrics spin-7-manifoldsarXiv posted 2 days ago

Conjecture that the conformal holonomy is exactly G2G_2G2​ for the non-conformally Einstein example