This article is cited in 3 scientific papers (total in 3 papers)
Regular and Quasiregular Isometric Flows on Riemannian Manifolds
V. N. Berestovskiia, Yu. G. Nikonorovb
a Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science
b Rubtsovsk Industrial Intitute, Branch of Altai State Technical University
We study the nontrivial Killing vector fields of constant length and the corresponding flows on smooth Riemannian manifolds. We describe the properties of the set of all points of finite (infinite) period for general isometric flows on Riemannian manifolds. It is shown that this flow is generated by an effective almost free isometric action of the group $S^1$ if there are no points of infinite or zero period. In the last case, the set of periods is at most countable and generates naturally an invariant stratification with closed totally geodesic strata; the union of all regular orbits is an open connected dense subset of full measure.
Riemannian manifold, Killing vector field, action of the circle, geodesic.
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Siberian Advances in Mathematics, 2008, 18:3, 153–162
V. N. Berestovskii, Yu. G. Nikonorov, “Regular and Quasiregular Isometric Flows on Riemannian Manifolds”, Mat. Tr., 10:2 (2007), 3–18; Siberian Adv. Math., 18:3 (2008), 153–162
Citation in format AMSBIB
\by V.~N.~Berestovskii, Yu.~G.~Nikonorov
\paper Regular and Quasiregular Isometric Flows on Riemannian Manifolds
\jour Mat. Tr.
\jour Siberian Adv. Math.
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Berestovskii V.N., Nikitenko E.V., Nikonorov Yu.G., “Classification of generalized normal homogeneous Riemannian manifolds of positive Euler characteristic”, Differential Geom. Appl., 29:4 (2011), 533–546
Yu. G. Nikonorov, “Killing vector fields and the curvature tensor of a Riemannian manifold”, Siberian Adv. Math., 24:3 (2014), 187–192
Nikonorov Yu.G., “Killing Vector Fields of Constant Length on Compact Homogeneous Riemannian Manifolds”, Ann. Glob. Anal. Geom., 48:4 (2015), 305–330
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