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Umbilicity of spacelike submanifolds of Minkowski space

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83703

Title: Umbilicity of spacelike submanifolds of Minkowski space
Authors: Izumiya, S. Browse this author
Pei, S. Browse this author
Fuster,M. C. Romero Browse this author
Issue Date: Jul-2002
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 558
Start Page: 1
End Page: 14
Abstract: We study some properties of spacelike submanifolds in Minkowski n­space all whose points are umbilic with respect to some normal field. As a consequence of these and some results contained in [l] we obtain that being v-umbilic with respect to a parallel lightlike normal field implies conformal flatness for submanifolds of dimension n 􀀩 2 2: 3. In the case of surfaces we relate the umbilicity condition to that of total semiumbilicity (degeneracy of the curvature ellipse at every point). Moreover, if the considered normal field is parallel we show that it is everywhere timelike, spacelike or lightlike if and only if the surface is included in a hyperbolic 3-space, a de Sitter 3-space or a 3-dimensional light cone respectively. We also give characterizations of total semiumbilicity for surfaces contained in hyperbolic 4-space, de Sitter 4-space and 4-dimensional light cone.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69307
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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