Invariants and flow geometry

J. González-Dávila; L. Vanhecke

Colloquium Mathematicae (1999)

  • Volume: 81, Issue: 1, page 33-50
  • ISSN: 0010-1354

Abstract

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We continue the study of Riemannian manifolds (M,g) equipped with an isometric flow ℱ ξ generated by a unit Killing vector field ξ. We derive some new results for normal and contact flows and use invariants with respect to the group of ξ-preserving isometries to charaterize special (M,g, ℱ ξ ), in particular Einstein, η-Einstein, η-parallel and locally Killing-transversally symmetric spaces. Furthermore, we introduce curvature homogeneous flows and flow model spaces and derive an algebraic characterization of Killing-transversally symmetric spaces by using the curvature tensor of special flow model spaces. All these results extend the corresponding theory in Sasakian geometry to flow geometry.

How to cite

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González-Dávila, J., and Vanhecke, L.. "Invariants and flow geometry." Colloquium Mathematicae 81.1 (1999): 33-50. <http://eudml.org/doc/210728>.

@article{González1999,
abstract = {We continue the study of Riemannian manifolds (M,g) equipped with an isometric flow $ℱ_ξ$ generated by a unit Killing vector field ξ. We derive some new results for normal and contact flows and use invariants with respect to the group of ξ-preserving isometries to charaterize special (M,g,$ℱ_ξ$), in particular Einstein, η-Einstein, η-parallel and locally Killing-transversally symmetric spaces. Furthermore, we introduce curvature homogeneous flows and flow model spaces and derive an algebraic characterization of Killing-transversally symmetric spaces by using the curvature tensor of special flow model spaces. All these results extend the corresponding theory in Sasakian geometry to flow geometry.},
author = {González-Dávila, J., Vanhecke, L.},
journal = {Colloquium Mathematicae},
keywords = {flow model spaces; normal, contact and curvature homogeneous flows; invariants and characterizations of special Riemannian manifolds; flows generated by a unit Killing vector field; curvature homogeneous flow; invariants; special Riemannian manifolds; Sasakian space; flow geometry},
language = {eng},
number = {1},
pages = {33-50},
title = {Invariants and flow geometry},
url = {http://eudml.org/doc/210728},
volume = {81},
year = {1999},
}

TY - JOUR
AU - González-Dávila, J.
AU - Vanhecke, L.
TI - Invariants and flow geometry
JO - Colloquium Mathematicae
PY - 1999
VL - 81
IS - 1
SP - 33
EP - 50
AB - We continue the study of Riemannian manifolds (M,g) equipped with an isometric flow $ℱ_ξ$ generated by a unit Killing vector field ξ. We derive some new results for normal and contact flows and use invariants with respect to the group of ξ-preserving isometries to charaterize special (M,g,$ℱ_ξ$), in particular Einstein, η-Einstein, η-parallel and locally Killing-transversally symmetric spaces. Furthermore, we introduce curvature homogeneous flows and flow model spaces and derive an algebraic characterization of Killing-transversally symmetric spaces by using the curvature tensor of special flow model spaces. All these results extend the corresponding theory in Sasakian geometry to flow geometry.
LA - eng
KW - flow model spaces; normal, contact and curvature homogeneous flows; invariants and characterizations of special Riemannian manifolds; flows generated by a unit Killing vector field; curvature homogeneous flow; invariants; special Riemannian manifolds; Sasakian space; flow geometry
UR - http://eudml.org/doc/210728
ER -

References

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