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5 papers · 1 filter
On the Structure of Lie Pseudo-Groups
Peter J. Olver, Juha Pohjanpelto, Francis Valiquette
We compare and contrast two approaches to the structure theory for Lie pseudo-groups, the first due to Cartan, and the second due to the first two authors. We argue that the latter…
Total curvature and isotopy of graphs in
Robert Gulliver, Sumio Yamada
Knot theory is the study of isotopy classes of embeddings of the circle into a 3-manifold, specifically . The Fáry-Milnor Theorem says that any curve in of total c…
(Semi-)Riemannian geometry of (para-)octonionic projective planes
Rowena Held, Iva Stavrov, Brian VanKoten
We use reduced homogeneous coordinates to study Riemannian geometry of the octonionic (or Cayley) projective plane. Our method extends to the para-octonionic (or split octonionic)…
Connections for general group actions
Debra Lewis, Nilima Nigam, Peter Olver
Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group…
A pinching estimate for solutions of the linearized Ricci flow system on 3-manifolds
Greg Anderson, Bennett Chow
We prove an estimate for solutions to the linearized Ricci flow system on closed 3-manifolds. This estimate is a generalization of Hamilton's pinching is preserved estimate for the…