On double-ruled hypersurfaces in 𝐑 4

Oldřich Kowalski; Zdeněk Vlášek

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 2, page 407-411
  • ISSN: 0010-2628

Abstract

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We classify locally the induced Riemannian metrics of all irreducible double-ruled hypersurfaces in 𝐑 4 .

How to cite

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Kowalski, Oldřich, and Vlášek, Zdeněk. "On double-ruled hypersurfaces in $\mathbf {R}^4$." Commentationes Mathematicae Universitatis Carolinae 38.2 (1997): 407-411. <http://eudml.org/doc/248110>.

@article{Kowalski1997,
abstract = {We classify locally the induced Riemannian metrics of all irreducible double-ruled hypersurfaces in $\mathbf \{R\}^4$.},
author = {Kowalski, Oldřich, Vlášek, Zdeněk},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Riemannian manifold; ruled hypersurface; induced Riemannian metrics; ruled hypersurface; Euclidean 4-space},
language = {eng},
number = {2},
pages = {407-411},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On double-ruled hypersurfaces in $\mathbf \{R\}^4$},
url = {http://eudml.org/doc/248110},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Kowalski, Oldřich
AU - Vlášek, Zdeněk
TI - On double-ruled hypersurfaces in $\mathbf {R}^4$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 2
SP - 407
EP - 411
AB - We classify locally the induced Riemannian metrics of all irreducible double-ruled hypersurfaces in $\mathbf {R}^4$.
LA - eng
KW - Riemannian manifold; ruled hypersurface; induced Riemannian metrics; ruled hypersurface; Euclidean 4-space
UR - http://eudml.org/doc/248110
ER -

References

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  1. Barbosa J.L.M., Delgado J.A., Ruled submanifolds of space forms with mean curvature of nonzero constant length, Amer. J. Math. 106 (1984), 763-780. (1984) Zbl0553.53010MR0749256
  2. Barbosa J.L.M., Jorge L.P.M., Dajczer M., Minimal ruled submanifolds of spaces of constant curvature, Indiana Univ. Math. J. 33 (1984), 531-547. (1984) MR0749313
  3. Boeckx E., Kowalski O., Vanhecke L., Riemannian manifolds of conullity two, World Scientific Publ., Singapore, 1996 (Monograph). Zbl0904.53006MR1462887
  4. Dajczer M., Gromoll D., Rigidity of complete Euclidean hypersurfaces, J. Diff. Geom. 31 (1990), 401-416. (1990) Zbl0667.53003MR1037409

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