Integral Linking para o espaço hiperbólico

Abstract

This research aimed to find a comprehensive formula that calculates the linking number between two submanifolds of a visible hypersurface of hyperbolic space, which will be defined in the text. The motivation for this was the article "HIGHER-DIMENSIONAL LINKING INTEGRALS " whose authors are Clayton Shonkwiler and David Shea Candle-Vick. Which article Shonkwiler and Vela-Vick derive an integral formula for two submanifolds of a visible hypersurfaces of Euclidean space. Trying to adapt the idea of them, we were behind a full formula for the hyperbolic case, following the same script, but using the geometric structure of the hyperbolic space. Moreover, it is noteworthy that the Shonkwiler article and Vela-Vick is quite succinct, leaving several arguments and unexplained passages, which also led us to go back to explain in more detail all the arguments of them and thus a " concept new " and very important had to be made, such a concept we call "conical variety," which is not a deferenciável variety of apparel and so we had to develop a little degree theory for such sets. Finally, we gave work to express " application of hyperbolic Gauss ", in order that it desempenhasse the same role that the application of Euclidean Gauss played in article Shonkwiler and Vela-Vick.