Normally flat semiparallel submanifolds in space forms as immersed semisymmetric Riemannian manifolds

Ülo Lumiste

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 2, page 243-260
  • ISSN: 0010-2628

Abstract

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By means of the bundle of orthonormal frames adapted to the submanifold as in the title an explicit exposition is given for these submanifolds. Two theorems give a full description of the semisymmetric Riemannian manifolds which can be immersed as such submanifolds. A conjecture is verified for this case that among manifolds of conullity two only the planar type (in the sense of Kowalski) is possible.

How to cite

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Lumiste, Ülo. "Normally flat semiparallel submanifolds in space forms as immersed semisymmetric Riemannian manifolds." Commentationes Mathematicae Universitatis Carolinae 43.2 (2002): 243-260. <http://eudml.org/doc/248965>.

@article{Lumiste2002,
abstract = {By means of the bundle of orthonormal frames adapted to the submanifold as in the title an explicit exposition is given for these submanifolds. Two theorems give a full description of the semisymmetric Riemannian manifolds which can be immersed as such submanifolds. A conjecture is verified for this case that among manifolds of conullity two only the planar type (in the sense of Kowalski) is possible.},
author = {Lumiste, Ülo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {semiparallel submanifolds; flat normal connection; semisymmetric Riemannian manifolds; manifolds of conullity two; semiparallel submanifolds; semisymmetric Riemannian manifolds},
language = {eng},
number = {2},
pages = {243-260},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Normally flat semiparallel submanifolds in space forms as immersed semisymmetric Riemannian manifolds},
url = {http://eudml.org/doc/248965},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Lumiste, Ülo
TI - Normally flat semiparallel submanifolds in space forms as immersed semisymmetric Riemannian manifolds
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 2
SP - 243
EP - 260
AB - By means of the bundle of orthonormal frames adapted to the submanifold as in the title an explicit exposition is given for these submanifolds. Two theorems give a full description of the semisymmetric Riemannian manifolds which can be immersed as such submanifolds. A conjecture is verified for this case that among manifolds of conullity two only the planar type (in the sense of Kowalski) is possible.
LA - eng
KW - semiparallel submanifolds; flat normal connection; semisymmetric Riemannian manifolds; manifolds of conullity two; semiparallel submanifolds; semisymmetric Riemannian manifolds
UR - http://eudml.org/doc/248965
ER -

References

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