Abstract
The aim of the paper is to give a classification up to isomorphism of (local or simply-connected global) Riemannian almost-product structures (i.e. O(n 1) × ... × O(n t)-structures) whose automorphism group has maximal dimension (the so-called ℳ-structures). The describing objects are Lie algebras with some additional structure, and the methods are mainly Lie algebraic. The results obtained are applied to determine all ℳ-structures on simply-connected spaces of constant curvature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cattani, E. H. and Mann, L. N., ‘Homogeneous Riemannian Manifolds with a Fixed Isotropy Representation’, J. Math. Soc. Japan 31 (1979), 535–552.
Gauchman, H., ‘On Maximally Mobile Riemannian Almost-Product Structures’, Tensor (N.S.) 31 (1977), 13–26.
Heintze, E., ‘On Homogeneous Manifolds of Negative Curvature’, Math. Ann. 211 (1974), 23–34.
Kobayashi, S., Transformation Groups in Differential Geometry, Springer, Berlin, Heidelberg, New York, 1972
Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, Interscience, New York, London, 1963 (vol. I), 1969 (vol. II).
Milnor, J., ‘Curvatures of Left Invariant Metrics on Lie Groups’, Advances Math. 21 (1976), 293–329.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Scheiderer, C. Riemannian almost-product structures with maximal mobility. Geom Dedicata 24, 109–122 (1987). https://doi.org/10.1007/BF00159751
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00159751