A GENERAL DESCRIPTION OF TOTALLY GEODESIC FOLIATIONS

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概要

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• We give some general concepts and results for totally geodesic foliations F on complete Riemannian manifolds. In particular, we reduce the problem to that of a generalization of the theory of principal connections. This enables us to show that the global geometry of F is related to certain sheaves of germs of local Killing vector fields for the Riemannian structure along the leaves. Further, we define a cohomology group {H<SUB>tg</SUB>}^ *, and natural mappings from {H<SUB>tg</SUB>}^ * into the de Rham cohomologies of the leaves, such that the characteristic classes in {H<SUB>tg</SUB>}^ * are mapped to the characteristic classes of the leaves.

• 東北大学大学院理学研究科数学専攻の論文

著者

• CAIRNS GRANT

  MATHÉMATIQUES UNIVERSITÉ DES SCIENCES ET TECHNIQUES DU LANGUEDOC PLACE E. BATAILLON

• CAIRNS GRANT

  MATHÉMATIQUES UNIVERSITÉ DES SCIENCES ET TECHNIQUES DU LANGUEDOC PLACE E. BATAILLON

関連論文

• A GENERAL DESCRIPTION OF TOTALLY GEODESIC FOLIATIONS

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