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Tag Archives: Riemannian geometry
Div, grad, curl and all this
The title of this post is a nod to the excellent and wellknown Div, grad, curl and all that by Harry Schey (and perhaps also to the lesserknown sequel to one of the more consoling histories of Great Britain), and the purpose … Continue reading
Posted in 3manifolds, Riemannian geometry
Tagged curl, div, exposition, grad, Riemannian geometry, vector field
12 Comments
Upper curvature bounds and CAT(K)
I am currently teaching a class at the University of Chicago on hyperbolic groups, and I have just introduced the concept of hyperbolic (geodesic) metric spaces. A geodesic metrix space is hyperbolic if for any geodesic triangle , and any … Continue reading
Posted in Hyperbolic geometry, Surfaces
Tagged CAT(K), comparison geometry, convexity, Jacobi fields, nonpositive curvature, Riemannian geometry
2 Comments
Second variation formula for minimal surfaces
If is a smooth function on a manifold , and is a critical point of , recall that the Hessian is the quadratic form on (in local coordinates, the coefficients of the Hessian are the second partial derivatives of at … Continue reading