Volume 143, Number 6, September 2023
|Number of page(s)
|Mathematical and interdisciplinary physics
|02 October 2023
Hyperbolic cones for casual diffeomorphisms
Department of Pure Mathematics, Shahid Bahonar University of Kerman - Kerman, Iran
Received: 31 July 2023
Accepted: 15 September 2023
This paper begins with introducing a new class of diffeomorphisms on pseudo-Riemannian manifolds which are called casual diffeomorphisms. We deduce a new pseudo-Riemannian metric via a casual diffeomorphism. We introduce a class of cones for a diffeomorphism, and we prove the existence of such cones for each p in a hyperbolic set of a casual diffeomorphism. As an example we find a hyperbolic casual diffeomorphism on a Schwarzschild pseudo-Riemannian manifold, and show that the whole manifold is a hyperbolic set for it.
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