葉層構造の基本関係式について

概要

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In recent years, there have been several studies of foliations from differentialgeometric aspects. Especially, many differential geometric properties of metricfoliations have been studied. In those studies, O'Neill's fundamental equationsplayed a central role. These equations are derived in the study of differentialgeometric properties of Riemannian submersions, which is defined by O'Neill andis a special class of metric foliations, which we do not treat in this paper. Forgeneral foliations, many results are also obtained. However, the approach is donefrom various view points depending on the mathematicians and, at present, thereseems to be no systematic approach.In this paper, we present some fundamental formulas for the differential geometricstudy of arbitrary foliations. These formulas turns out to be useful especiallywhen curvature conditions are given. We give new proofs of many known resultsfrom this view points, and also give some newresults.
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