2022/07/04 by Antonio J. Di Scala, Di Scala, Antonio J., Carlos Olmos +3
Mathematics · Physics and Astronomy · #53C30 #53C40 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2207.01746
openalex publication_date 2022/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We find new conditions that the existence of nullity of the curvature tensor of an irreducible homogeneous space M=G/H imposes on the Lie algebra \mathfrak g of G and on the Lie algebra \mathfrak g of the full isometry group of M. Namely, we prove that there exists a transvection of M in the direction of any element of the nullity, possibly by enlarging the presentation group G. Moreover, we prove that these transvections generate an abelian ideal of \mathfrak g. These results constitute a substantial improvement on the structure theory developed in \citeDOV. In addition we construct examples of homogeneous Riemannian spaces with non-trivial nullity, where G is a non-solvable group, answering a natural open question. Such examples admit (locally homogeneous) compact quotients. In the case of co-nullity 3 we give an explicit description of the isometry group of any homogeneouslocally irreducible Riemannian manifold with nullity.