TOTALLY GEODESIC SUBSETS IN THE MANIFOLD OF DIRECTIONS OF PHYSICAL SPACE


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Abstract

Let M0 be the Minkowski 4-space, let Λ2(M0) denote the second exterior power of M0 equipped with a structure of a pseudo-Euclidean space with signature (3, 3), let K0(M0) ⊂ Λ2 M0 be the light cone, and let G1 ⊂ Λ2(M0) be the set of the oriented 2-planes meeting the interior of K0(M0). Four types of totally geodesic two-manifolds in G1 are described such that manifolds of one type are pairwise congruent as subsets in Λ2(M0), while manifolds of different types are not. Models of such manifolds in the disk D3 are constructed. An explicit formula for the curvature tensor of G1 is given. Bibliography: 6 titles.

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