2011/10/28 by Marco Castrillón López, M. Castrillon Lopez, Lopez, M. Castrillon +3
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG
paper · pdf · doi:10.48550/arxiv.1110.6335
arxiv created 2011/10/28 · openalex publication_date 2011/10/28 · arxiv updated 2011/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this article is the study of homogeneous Riemannian structure tensors within the framework of reduction under a group H of isometries. In a first result, H is a normal subgroup of the group of symmetries associated to the reducing tensor S. The situation when H is any group acting freely is analyzed in a second result. The invariant classes of homogeneous tensors are also investigated when reduction is performed. It turns out that the geometry of the fibres is involved in the preservation of some of them. Some classical examples illustrate the theory. Finally, the reduction procedure is applied to fiberings of almost contact manifolds over almost Hermitian manifolds. If the structure is moreover Sasakian, the obtained reduced tensor is homogeneous Kähler.