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Title: Weakly disk-homogeneous spaces
Authors: Bueken, Peter ×
Vanhecke, Lieven #
Issue Date: 1998
Publisher: Akademiai kiado
Series Title: Acta mathematica hungarica vol:81 issue:3 pages:249-270
Abstract: Naturally reductive Riemannian homogeneous spaces and more generally, g.o. spaces, have the property that the volume of a geodesic disk normal to a geodesic and with center on that geodesic remains constant when the center moves along that central geodesic. Riemannian manifolds having that property for arbitrary geodesics and all sufficiently small geodesic disks are called weakly disk-homogeneous. Since, up to local isometries, there are no other examples known for dimension > 2, we investigate whether a possible converse holds or not. Besides some general results, we give a positive answer for three-dimensional and for several classes of four-dimensional manifolds. Some related results are discussed, in particular about four-dimensional Einstein C-spaces.
ISSN: 0236-5294
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Geometry Section
Mathematics - miscellaneous
× corresponding author
# (joint) last author

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