Parallel and totally geodesic hypersurfaces of 5-dimensional 2-step homogeneous nilmanifolds

Mehri Nasehi

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 2, page 547-559
  • ISSN: 0011-4642

Abstract

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In this paper we study parallel and totally geodesic hypersurfaces of two-step homogeneous nilmanifolds of dimension five. We give the complete classification and explicitly describe parallel and totally geodesic hypersurfaces of these spaces. Moreover, we prove that two-step homogeneous nilmanifolds of dimension five which have one-dimensional centre never admit parallel hypersurfaces. Also we prove that the only two-step homogeneous nilmanifolds of dimension five which admit totally geodesic hypersurfaces have three-dimensional centre.

How to cite

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Nasehi, Mehri. "Parallel and totally geodesic hypersurfaces of 5-dimensional 2-step homogeneous nilmanifolds." Czechoslovak Mathematical Journal 66.2 (2016): 547-559. <http://eudml.org/doc/280091>.

@article{Nasehi2016,
abstract = {In this paper we study parallel and totally geodesic hypersurfaces of two-step homogeneous nilmanifolds of dimension five. We give the complete classification and explicitly describe parallel and totally geodesic hypersurfaces of these spaces. Moreover, we prove that two-step homogeneous nilmanifolds of dimension five which have one-dimensional centre never admit parallel hypersurfaces. Also we prove that the only two-step homogeneous nilmanifolds of dimension five which admit totally geodesic hypersurfaces have three-dimensional centre.},
author = {Nasehi, Mehri},
journal = {Czechoslovak Mathematical Journal},
keywords = {hypersurface; totally geodesic hypersurface; parallel geodesic hypersurfaces; two-step homogeneous nilmanifold},
language = {eng},
number = {2},
pages = {547-559},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Parallel and totally geodesic hypersurfaces of 5-dimensional 2-step homogeneous nilmanifolds},
url = {http://eudml.org/doc/280091},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Nasehi, Mehri
TI - Parallel and totally geodesic hypersurfaces of 5-dimensional 2-step homogeneous nilmanifolds
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 547
EP - 559
AB - In this paper we study parallel and totally geodesic hypersurfaces of two-step homogeneous nilmanifolds of dimension five. We give the complete classification and explicitly describe parallel and totally geodesic hypersurfaces of these spaces. Moreover, we prove that two-step homogeneous nilmanifolds of dimension five which have one-dimensional centre never admit parallel hypersurfaces. Also we prove that the only two-step homogeneous nilmanifolds of dimension five which admit totally geodesic hypersurfaces have three-dimensional centre.
LA - eng
KW - hypersurface; totally geodesic hypersurface; parallel geodesic hypersurfaces; two-step homogeneous nilmanifold
UR - http://eudml.org/doc/280091
ER -

References

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