Ciclos principais hiperbólicos em hipersuperfícies do R4

Abstract

Based on the article “Hyperbolic Main Cycles on Hypersurface of R4”, Garcia, see [4], we will study the bending lines in the vicinity of a main loop, closed bending line, a hypersurface immersed in R4. For this, we will define the Poincaré transformation associated with the cycle and calculate its derivative. With this analysis, we show under what conditions we can become hyperbolic, with a small deformation in the immersion, a major cycle given. Finally, we will build an example of a hypersurface containing a hyperbolic primary cycle, based on the article “Surfaces Around Closed Main Curvature Lines, an Inverse Problem." Garcia, Mello and Sotomayor, see [5].