Submanifolds with totally geodesic Gauss image

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1984 English Publisher:Springer Science and Business Media LLCJournal:Geometriae Dedicata, volume 15 (issn: 0046-5755, eissn: 1572-9168,

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Authors: Chen, Bang-Yen; Yamaguchi, Seiichi;

doi: 10.1007/bf00147654

Submanifolds with totally geodesic Gauss image

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Abstract

This is a continuation for higher dimensions of the author's paper [Indiana Univ. Math. J. 32, 143-154 (1983; Zbl 0471.53004]. Beyond the property of totally geodesic Gauss map (into the Grassmannian) additional assumptions like ''conformal Gauss map'' or ''flat normal connection'' are needed to obtain significant consequences.

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Keywords

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Local submanifolds, totally geodesic, Gauss map, conformally flat, Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces

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