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Conformal vector fields on Finsler manifolds

József Szilasi, Anna Tóth (2011)

Communications in Mathematics

Applying concepts and tools from classical tangent bundle geometry and using the apparatus of the calculus along the tangent bundle projection (‘pull-back formalism’), first we enrich the known lists of the characterizations of affine vector fields on a spray manifold and conformal vector fields on a Finsler manifold. Second, we deduce consequences on vector fields on the underlying manifold of a Finsler structure having one or two of the mentioned geometric properties.

Constant scalar curvature hypersurfaces with spherical boundary in Euclidean space.

Luis J. Alías, J. Miguel Malacarne (2002)

Revista Matemática Iberoamericana

It is still an open question whether a compact embedded hypersurface in the Euclidean space with constant mean curvature and spherical boundary is necessarily a hyperplanar ba1l or a spherical cap, even in the simplest case of a compact constant mean curvature surface in R3 bounded by a circle. In this paper we prove that this is true for the case of the scalar curvature. Specifica1ly we prove that the only compact embedded hypersurfaces in the Euclidean space with constant scalar curvature and...

Constructing isothermal curvature line coordinates on surfaces which admit them

Eugenio Aulisa, Magdalena Toda, Zeynep Kose (2013)

Open Mathematics

Isothermic parameterizations are synonyms of isothermal curvature line parameterizations, for surfaces immersed in Euclidean spaces. We provide a method of constructing isothermic coordinate charts on surfaces which admit them, starting from an arbitrary chart. One of the primary applications of this work consists of numerical algorithms for surface visualization.

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