We prove that minimal (extrinsically) homogeneous submanifolds of the Euclidean space are totally geodesic. As an application, we obtain that a complex homogeneous submanifold of CN must be totally ...geodesic. PUBLICATION ABSTRACT
In this paper we establish the connections between two different extensions of
Z
4
-linearity for binary Hamming spaces. We present both notions – propelinearity and
G-linearity – in the context of ...isometries and group actions, taking the viewpoint of geometrically uniform codes extended to discrete spaces. We show a double inclusion relation: binary
G-linear codes are propelinear codes, and translation-invariant propelinear codes are
G-linear codes.
Let M be a connected homogeneous Riemannian manifold, G the identity component of the full isometry group of M and H a transitive connected subgroup of G. G = HL, where L is the isotropy group at ...some point of M. M is naturally identified with the homogeneous space H/H ∩ L endowed with a suitable left-invariant Riemannian metric. This paper addresses the problem: Given a realization of M as a Riemannian homogeneous space of a connected Lie group H, describe the structure of the full connected isometry group G in terms of H. This problem has already been studied in case H is compact, semisimple of noncompact type, or solvable. We use the fact that every Lie group is a product of subgroups of these three types in order to study the general case.
It is shown that the trajectories of an isometry group admit orthogonal surfaces if the sub-group of stability leaves no vector in the tangent space of the trajectories fixed. A necessary and ...sufficient condition is given that the trajectories of an Abelian group admit orthogonal surfaces.
In spacetimes which admit an Abelian G
of isometries, the trajectories admit orthogonal 2-surfaces if a timelike congruence exists with the following properties: the curves lie in the trajectories and are invariant under G
; ω
and ü
are linearly independent and orthogonal to the trajectories.
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