1. See the article on orientability for more on orientations of manifolds. 2. Thus the existence of a volume form is equivalent to orientability . 3. Orientability and orientations can also be expressed in terms of the tangent bundle.4. It is possible to drop the orientability condition and work with coefficients instead. 5. The notion of orientability can be generalised to higher-dimensional manifolds as well. 6. The existence of a volume form is therefore equivalent to orientability of the manifold. 7. In other words, Euler characteristic and orientability completely classify closed surfaces up to homeomorphism. 8. Volume forms and tangent vectors can be combined to give yet another description of orientability . 9. In Lorentzian geometry, there are two kinds of orientability : space orientability and time orientability. 10. In Lorentzian geometry, there are two kinds of orientability : space orientability and time orientability.
Mobile