Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix

Yana Alexieva; Stefan Ivanov

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 2, page 129-140
  • ISSN: 0044-8753

Abstract

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Riemannian manifolds for which a natural skew-symmetric curvature operator has constant eigenvalues on helices are studied. A local classification in dimension three is given. In the three dimensional case one gets all locally symmetric spaces and all Riemannian manifolds with the constant principal Ricci curvatures r 1 = r 2 = 0 , r 3 0 , which are not locally homogeneous, in general.

How to cite

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Alexieva, Yana, and Ivanov, Stefan. "Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix." Archivum Mathematicum 035.2 (1999): 129-140. <http://eudml.org/doc/248353>.

@article{Alexieva1999,
abstract = {Riemannian manifolds for which a natural skew-symmetric curvature operator has constant eigenvalues on helices are studied. A local classification in dimension three is given. In the three dimensional case one gets all locally symmetric spaces and all Riemannian manifolds with the constant principal Ricci curvatures $r_1 = r_2 = 0, r_3 \ne 0$, which are not locally homogeneous, in general.},
author = {Alexieva, Yana, Ivanov, Stefan},
journal = {Archivum Mathematicum},
keywords = {helix; constant eigenvalues of the curvature operator; locally symmetric spaces; curvature homogeneous spaces; helix; constant eigenvalues of the curvature},
language = {eng},
number = {2},
pages = {129-140},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix},
url = {http://eudml.org/doc/248353},
volume = {035},
year = {1999},
}

TY - JOUR
AU - Alexieva, Yana
AU - Ivanov, Stefan
TI - Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 2
SP - 129
EP - 140
AB - Riemannian manifolds for which a natural skew-symmetric curvature operator has constant eigenvalues on helices are studied. A local classification in dimension three is given. In the three dimensional case one gets all locally symmetric spaces and all Riemannian manifolds with the constant principal Ricci curvatures $r_1 = r_2 = 0, r_3 \ne 0$, which are not locally homogeneous, in general.
LA - eng
KW - helix; constant eigenvalues of the curvature operator; locally symmetric spaces; curvature homogeneous spaces; helix; constant eigenvalues of the curvature
UR - http://eudml.org/doc/248353
ER -

References

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