He holds a degree and a master's degree in pure mathematics from the Federal University of São Carlos. He has experience in the areas of Differential Geometry and Geometric Analysis. (Source: Lattes Curriculum)
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Darboux hypersurfaces are those obtained by moving a submanifold of codimension two by a one-parameter family of isometries of the ambient manifold. Important particular examples of Darboux hypersurfaces are the ruled hypersurfaces (in particular, cylindrical, conical and helicoidal hypersurfaces), translational and homothetic hypersurfaces, sphere-foliated hypersurfaces (in particular, r…
Geometric Analysis is a frontier area of Mathematics that, as the name implies, relates Analysis to Geometry. In a nutshell, Geometric Analysis uses the theory of Partial Differential Equations (especially Elliptic theory) to solve problems of Geometry and/or Differential Topology.The use of analytical techniques in Geometry is not new, but it gained much prominence from the 80's (and rem…
A Weingarten surface S in a three-dimensional Riemannian (or semi-Riemannian) manifold is a regular surface whose principal curvatures k1 and k2 verify a relationship (usually polynomial, but not necessarily) P (k1, k2) = 0. Since the mean and Gaussian curvatures H and K determine/are determined by the principal curvatures of S, the relation P can always be rewritten in the form Q (H, K) …
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