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Ricci solitons on compact three-manifolds
Abstract In this short article we show that there are no compact three-dimensional Ricci solitons other than spaces of constant curvature. This generalizes a result obtained for surfaces by HamiltonExpand
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Cartan for beginners
Moving frames and exterior differential systems Euclidean geometry and Riemannian geometry Projective geometry Cartan-Kahler I: Linear algebra and constant-coefficient homogeneous systemsExpand
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Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems, Second Edition
p. 17, Def. 1.6.4, line 2 change ω|e to ωe p. 17, line -1 change Ada−1 to Ad(a −1) p. 18, Def. 1.6.9 right-hand side of displayed equation should read [ω(X), θ(Y )] − [ω(Y ), θ(X)] (not +) p. 19,Expand
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BÄCKLUND TRANSFORMATIONS AND KNOTS OF CONSTANT TORSION
The Backlund transformation for pseudospherical surfaces, which is equivalent to that of the sine-Gordon equation, can be restricted to give a transformation on space curves that preserves constantExpand
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New examples of complete Ricci solitons
The Ricci soliton condition reduces to a set of ODEs when one assumes that the metric is a doubly-warped product of a ray with a sphere and an Einstein manifold. If the Einstein manifold has positiveExpand
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Hopf Hypersurfaces of Small Hopf Principal Curvature in CH^2
Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex hyperbolic space CH^2 with any specified value of the Hopf principalExpand
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Knot Types, Homotopies and Stability of Closed Elastic Rods
The energy minimization problem associated to uniform, isotropic, linearly elastic rods leads to a geometric variational problem for the rod centerline, whose solutions include closed, knottedExpand
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A d’Alembert Formula for Hopf Hypersurfaces
A Hopf hypersurface in complex hyperbolic space $${\mathbb{C}{\rm H}^n}$$ is one for which the complex structure applied to the normal vector is a principal direction at each point. In this paper,Expand
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Remarks on KdV-type flows on star-shaped curves
Abstract We study the relation between the centro-affine geometry of star-shaped planar curves and the projective geometry of parametrized maps into R P 1 . We show that projectivization induces aExpand
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