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キーワード:
Mathematics, Differential Geometry, math.DG
要旨:
For an asymptotically locally Euclidean (ALE) or asymptotically locally flat
(ALF) gravitational instanton $(M,g)$ with toric symmetry, we express the
signature of $(M,g)$ directly in terms of its rod structure. Applying
Hitchin$\unicode{x2013}$Thorpe-type inequalities for Ricci-flat ALE/ALF
manifolds, we formulate necessary conditions that the rod structures of toric
ALE/ALF instantons must satisfy, as a step toward a classification of such
spaces. Finally, we apply these results to the study of rod structures with
three turning points.
