Euclidean hypersurfaces with a totally geodesic foliation of codimension one

M. Dajczer; V. Rovenski; R. Tojeiro

doi:10.1007/s10711-014-9964-4

Euclidean hypersurfaces with a totally geodesic foliation of codimension one

M. Dajczer
, V. Rovenski
, R. Tojeiro

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We classify the hypersurfaces of Euclidean space that carry a totally geodesic foliation with complete leaves of codimension one. In particular, we show that rotation hypersurfaces with complete profiles of codimension one are characterized by their warped product structure. The local version of the problem is also considered.

Original language	English
Article number	9
Pages (from-to)	215-224
Number of pages	10
Journal	Geometriae Dedicata
Volume	176
Issue number	1
DOIs	https://doi.org/10.1007/s10711-014-9964-4
State	Published - 22 Jun 2015

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media Dordrecht.

Keywords

Euclidean hypersurfaces
Partial tubes
Rotation hypersurfaces
Totally geodesic foliations

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1007/s10711-014-9964-4

Cite this

@article{20252d159cbb4ebc99d5b1a4c6dc8050,

title = "Euclidean hypersurfaces with a totally geodesic foliation of codimension one",

abstract = "We classify the hypersurfaces of Euclidean space that carry a totally geodesic foliation with complete leaves of codimension one. In particular, we show that rotation hypersurfaces with complete profiles of codimension one are characterized by their warped product structure. The local version of the problem is also considered.",

keywords = "Euclidean hypersurfaces, Partial tubes, Rotation hypersurfaces, Totally geodesic foliations",

author = "M. Dajczer and V. Rovenski and R. Tojeiro",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media Dordrecht.",

year = "2015",

month = jun,

day = "22",

doi = "10.1007/s10711-014-9964-4",

language = "English",

volume = "176",

pages = "215--224",

journal = "Geometriae Dedicata",

issn = "0046-5755",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Euclidean hypersurfaces with a totally geodesic foliation of codimension one

AU - Dajczer, M.

AU - Rovenski, V.

AU - Tojeiro, R.

PY - 2015/6/22

Y1 - 2015/6/22

N2 - We classify the hypersurfaces of Euclidean space that carry a totally geodesic foliation with complete leaves of codimension one. In particular, we show that rotation hypersurfaces with complete profiles of codimension one are characterized by their warped product structure. The local version of the problem is also considered.

AB - We classify the hypersurfaces of Euclidean space that carry a totally geodesic foliation with complete leaves of codimension one. In particular, we show that rotation hypersurfaces with complete profiles of codimension one are characterized by their warped product structure. The local version of the problem is also considered.

KW - Euclidean hypersurfaces

KW - Partial tubes

KW - Rotation hypersurfaces

KW - Totally geodesic foliations

UR - https://www.scopus.com/pages/publications/84893170201

U2 - 10.1007/s10711-014-9964-4

DO - 10.1007/s10711-014-9964-4

M3 - Article

AN - SCOPUS:84893170201

SN - 0046-5755

VL - 176

SP - 215

EP - 224

JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

M1 - 9

ER -

Euclidean hypersurfaces with a totally geodesic foliation of codimension one

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this