Homogeneous Riemannian structures in dimension three
نویسندگان
چکیده
Abstract In this note, we determine all the homogeneous structures on non-symmetric three-dimensional Riemannian Lie groups. We show that a group admits non-canonical structure if and only its isometry has dimension four.
منابع مشابه
Local properties of almost-Riemannian structures in dimension 3
A 3D almost-Riemannian manifold is a generalized Riemannian manifold defined locally by 3 vector fields that play the role of an orthonormal frame, but could become collinear on some set Z called the singular set. Under the Hormander condition, a 3D almost-Riemannian structure still has a metric space structure, whose topology is compatible with the original topology of the manifold. Almost-Rie...
متن کاملSome Einstein Homogeneous Riemannian Fibrations
We study the existence of projectable G-invariant Einstein metrics on the total space of G-equivariant fibrations M = G/L → G/K, for a compact connected semisimple Lie group G. We obtain necessary conditions for the existence of such Einstein metrics in terms of appropriate Casimir operators, which is a generalization of the result by Wang and Ziller about Einstein normal metrics. We describe b...
متن کاملFlat Homogeneous Pseudo-Riemannian Manifolds
The complete homogeneous pseudo-Riemannian manifolds of constant non-zero curvature were classified up to isometry in 1961 [1]. In the same year, a structure theory [2] was developed for complete fiat homogeneous pseudo-Riemannian manifolds. Here that structure theory is sharpened to a classification. This completes the classification of complete homogeneous pseudo-Riemannian manifolds of arbit...
متن کاملThe Kinematic Formula in Riemannian Homogeneous Spaces
Let G be a Lie group and K a compact subgroup of G. Then the homogeneous space G/K has an invariant Riemannian metric and an invariant volume form ΩG. Let M and N be compact submanifolds of G/K, and I(M ∩ gN) an “integral invariant” of the intersection M ∩ gN . Then the integral
متن کاملCurvature Homogeneous Pseudo-riemannian Manifolds Which Are Not Locally Homogeneous
We construct a family of balanced signature pseudo-Riemannian manifolds, which arise as hypersurfaces in flat space, that are curvature homogeneous, that are modeled on a symmetric space, and that are not locally homogeneous.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas
سال: 2023
ISSN: ['1578-7303', '1579-1505']
DOI: https://doi.org/10.1007/s13398-023-01404-y