Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds (eBook)

J. L Flores (Autor)

eBook Download: PDF

76 Seiten
American Mathematical Society (Verlag)
978-1-4704-1064-3 (ISBN)

Infos

Recently, the old notion of causal boundary for a spacetime $V$ has been redefined consistently. The computation of this boundary $/partial V$ on any standard conformally stationary spacetime $V=/mathbb{R}/times M$, suggests a natural compactification $M_B$ associated to any Riemannian metric on $M$ or, more generally, to any Finslerian one. The corresponding boundary $/partial_BM$ is constructed in terms of Busemann-type functions. Roughly, $/partial_BM$ represents the set of all the directions in $M$ including both, asymptotic and "e;finite"e; (or "e;incomplete"e;) directions. This Busemann boundary $/partial_BM$ is related to two classical boundaries: the Cauchy boundary $/partial_{C}M$ and the Gromov boundary $/partial_GM$. The authors' aims are: (1) to study the subtleties of both, the Cauchy boundary for any generalized (possibly non-symmetric) distance and the Gromov compactification for any (possibly incomplete) Finsler manifold, (2) to introduce the new Busemann compactification $M_B$, relating it with the previous two completions, and (3) to give a full description of the causal boundary $/partial V$ of any standard conformally stationary spacetime.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 1-4704-1064-8 / 1470410648
• ISBN-13: 978-1-4704-1064-3 / 9781470410643