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In [4], R. Hamilton has proved that if a compact manifold M of dimension three admits a C ∞ Riemannian metric g 0 with positive Ricci curvature, then it also admits a metric g with constant positive sectional curvature, and is thus a quotient of the sphere S 3. In fact, he shows that the original metric can be deformed into the constant-curvature metric by… (More)

Introduction. A number of authors [C], [DW1], [DW2], [L], [T] have studied minimal isometric immersions of Riemannian manifolds into round spheres, and in particular of round spheres into round spheres. As was observed by T. Takahashi [T], if Φ: M → S N (r) ⊂ R N +1 is such a minimal immersion, then the components of Φ must be eigenfuctions of the Laplace… (More)

- Jason Cantarella, Dennis DeTurck, Herman Gluck
- The American Mathematical Monthly
- 2002

- Dennis Deturck, Herman Gluck, +7 authors Vela-Vick
- 2009

To Manfredo do Carmo in friendship and admiration, on his 80 th birthday Abstract. Three-component links in the 3-dimensional sphere were classified up to link homotopy by John Milnor in his senior thesis, published in 1954. A complete set of invariants is given by the pairwise linking numbers p, q and r of the components, and by the residue class of one… (More)

- J R Senior, M F Johnson, D M DeTurck, F Bazzoli, E Roda
- Gastroenterology
- 1990

The rate of decrease of gallstone diameter appeared to be linear with oral bile acid treatment time, as estimated by inspection of graphic data of individual patient serial oral cholecystograms. A theoretical basis for this model was derived. The hypothesis of diameter decrease proportional to treatment time was tested with data from 223 patients with… (More)

The writhing number of a curve in Euclidean 3-space, introduced by C˘ alug˘ areanu (1959-61) and named by Fuller (1971), is the standard measure of the extent to which the curve wraps and coils around itself; it has proved its importance for molecular biologists in the study of knotted duplex DNA and of the enzymes which affect it. The helicity of a vector… (More)

To Julius Shaneson on the occasion of his 60th birthday

- Jason Cantarella, Dennis DeTurck, Herman Gluck, Mikhail Teytel
- 1998

The helicity of a smooth vector field defined on a domain in 3-space is the standard measure of the extent to which the field lines wrap and coil around one another; it plays important roles in fluid mechanics, magnetohy-drodynamics and plasma physics. In this report we show how the relation between energy and helicity of a vector field is influenced by the… (More)

For (M, g) a compact Riemannian manifold, we consider the spectra of the Laplace-Beltrami operator and of the Schrödinger operator "Laplacian plus potential" acting on L (M, g). Two Riemannian manifolds are said to be isospectral if their associated Laplacians have the same spectra, and two potentials on the same Riemannian manifold are said to be… (More)

- DENNIS DETURCK, HERMAN GLUCK, +4 authors DAVID SHEA VELA-VICK
- 2013

We describe a new approach to triple linking invariants and integrals, aiming for a simpler, wider and more natural applicability to the search for higher order helicities. To each three-component link in Euclidean 3–space, we associate a generalized Gauss map from the 3–torus to the 2–sphere, and show that the pairwise linking numbers and Milnor triple… (More)