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ArticleOriginal scientific text

Title

Invariants and flow geometry

Authors 1, 2

Affiliations

  1. Departamento de Matemática Fundamental, Sección de Geometría y Topología, Universidad de La Laguna, La Laguna, Spain
  2. Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium

Abstract

We continue the study of Riemannian manifolds (M,g) equipped with an isometric flow ℱξ 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,ℱξ), 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.

Keywords

ENG
flow model spaces, normal, contact and curvature homogeneous flows, invariants and characterizations of special Riemannian manifolds, flows generated by a unit Killing vector field

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Colloquium Mathematicum
1999/81/1
Export to PBN, Opens in new tab
Pages:
33-50
Main language of publication
English
Received
1998-12-17
Published
1999
Exact and natural sciences