Geometric mean curvature lines on surfaces immersed in
Ronaldo Garcia, Jorge Sotomayor (2002)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Displaying similar documents to “Examples of sectional curvature with prescribed symmetry on $3$-manifolds”
Geometric mean curvature lines on surfaces immersed in
Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres
Karsten Grove, Luigi Verdiani, Burkhard Wilking, Wolfgang Ziller (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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In contrast to the homogeneous case, we show that there are compact cohomogeneity one manifolds that do not support invariant metrics of non-negative sectional curvature. In fact we exhibit infinite families of such manifolds including the exotic Kervaire spheres. Such examples exist for any codimension of the singular orbits except for the case when both are equal to two, where existence of non-negatively curved metrics is known.
The volume of geodesic disks in a Riemannian manifold
Oldřich Kowalski, Lieven Vanhecke (1985)
Czechoslovak Mathematical Journal
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Doubling constant mean curvature tori in S
Adrian Butscher, Frank Pacard (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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The Clifford tori in constitute a one-parameter family of flat, two-dimensional, constant mean curvature (CMC) submanifolds. This paper demonstrates that new, topologically non-trivial CMC surfaces resembling a pair of neighbouring Clifford tori connected at a sub-lattice consisting of at least two points by small catenoidal bridges can be constructed by perturbative PDE methods. That is, one can create a submanifold that has almost everywhere constant mean curvature by gluing a re-scaled...