Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds
Seiten
2013
American Mathematical Society (Verlag)
978-0-8218-8775-2 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-8775-2 (ISBN)
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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 ``finite'' (or ``incomplete'') 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 generalised (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.
Erscheint lt. Verlag | 12.9.2014 |
---|---|
Reihe/Serie | Memoirs of the American Mathematical Society |
Verlagsort | Providence |
Sprache | englisch |
Gewicht | 300 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
ISBN-10 | 0-8218-8775-0 / 0821887750 |
ISBN-13 | 978-0-8218-8775-2 / 9780821887752 |
Zustand | Neuware |
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