Complete classification of parallel Lorentz surfaces in neutral pseudo hyperbolic 4-space

Bang-Yen Chen

Open Mathematics, Tome 8 (2010), p. 706-734 / Harvested from The Polish Digital Mathematics Library

Résumé

A Lorentz surface of an indefinite space form is called a parallel surface if its second fundamental form is parallel with respect to the Van der Waerden-Bortolotti connection. Such surfaces are locally invariant under the reflection with respect to the normal space at each point. Parallel surfaces are important in geometry as well as in general relativity since extrinsic invariants of such surfaces do not change from point to point. Recently, parallel Lorentz surfaces in 4D neutral pseudo Euclidean 4-space 𝔼24 and in neutral pseudo 4-sphere S 24 (1) were classified in [14] and in [10], respectively. In this paper, we completely classify parallel Lorentz surfaces in neutral pseudo hyperbolic 4-space H 24 (−1). Our main result states that there are 53 families of parallel Lorentz surfaces in H 24 (−1). Conversely, every parallel Lorentz surface in H 24 (−1) is obtained from the 53 families. As an immediate by-product, we achieve the complete classification of all parallel Lorentz surfaces in 4D neutral indefinite space forms.

Détail

Publié le : 2010-01-01

Zbl 1210.53058

EUDML-ID : urn:eudml:doc:269341

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