Given two points of a generalized Robertson-Walker space-time, the existence, multiplicity and causal character of geodesics connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on the fiber, and Morse-type relations are obtained. Applicat
Spaces of geodesics: products, coverings, connectedness
โ Scribed by John K. Beem; Robert J. Low; Phillip E. Parker
- Book ID
- 104653334
- Publisher
- Springer
- Year
- 1996
- Tongue
- English
- Weight
- 824 KB
- Volume
- 59
- Category
- Article
- ISSN
- 0046-5755
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โฆ Synopsis
We continue our study of the space of geodesics of a manifold with linear connection. We obtain sufficient conditions for a product to have a space of geodesics which is a manifold. We investigate the relationship of the space of geodesics of a covering manifold to that of the base space. We obtain sufficient conditions for a space to be geodesically connected in terms of the topology of its space of geodesics.
๐ SIMILAR VOLUMES
In this paper we use a variational approach in order to prove the geodesic connectedness of some Gรถdel type space-times; moreover direct methods allow to prove the geodesic connectedness of the Gรถdel Universe. At last a result of geodesic completeness is given.