Constant Angle Surfaces in Lorentzian Berger Spheres
In this work, we study helix spacelike and timelike surfaces in the Lorentzian Berger sphere S ε 3 , that is the three-dimensional sphere endowed with a 1-parameter family of Lorentzian metrics, obtained by deforming the round metric on S 3 along the fibers of the Hopf fibration S 3 → S 2 ( 1 / 2 )...
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| Veröffentlicht in: | The Journal of Geometric Analysis 2019-04, Vol.29 (2), p.1456-1478 |
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| container_issue | 2 |
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| container_title | The Journal of Geometric Analysis |
| container_volume | 29 |
| creator | Onnis, Irene I. Passos Passamani, Apoena Piu, Paola |
| description | In this work, we study helix spacelike and timelike surfaces in the Lorentzian Berger sphere
S
ε
3
, that is the three-dimensional sphere endowed with a 1-parameter family of Lorentzian metrics, obtained by deforming the round metric on
S
3
along the fibers of the Hopf fibration
S
3
→
S
2
(
1
/
2
)
by
-
ε
2
. Our main result provides a characterization of the helix surfaces in
S
ε
3
using the symmetries of the ambient space and a general helix in
S
ε
3
, with axis the infinitesimal generator of the Hopf fibers. Also, we construct some explicit examples of helix surfaces in
S
ε
3
. |
| doi_str_mv | 10.1007/s12220-018-0044-0 |
| format | Article |
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S
ε
3
, that is the three-dimensional sphere endowed with a 1-parameter family of Lorentzian metrics, obtained by deforming the round metric on
S
3
along the fibers of the Hopf fibration
S
3
→
S
2
(
1
/
2
)
by
-
ε
2
. Our main result provides a characterization of the helix surfaces in
S
ε
3
using the symmetries of the ambient space and a general helix in
S
ε
3
, with axis the infinitesimal generator of the Hopf fibers. Also, we construct some explicit examples of helix surfaces in
S
ε
3
.</description><identifier>ISSN: 1050-6926</identifier><identifier>EISSN: 1559-002X</identifier><identifier>DOI: 10.1007/s12220-018-0044-0</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Convex and Discrete Geometry ; Deformation ; Differential Geometry ; Dynamical Systems and Ergodic Theory ; Fourier Analysis ; Geometry ; Global Analysis and Analysis on Manifolds ; Mathematics ; Mathematics and Statistics</subject><ispartof>The Journal of Geometric Analysis, 2019-04, Vol.29 (2), p.1456-1478</ispartof><rights>Mathematica Josephina, Inc. 2018</rights><rights>COPYRIGHT 2019 Springer</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-1e97b258162aa8abba70380c8f7d2ea6d44aa61f21c3f330668a3cda521e8a0f3</citedby><cites>FETCH-LOGICAL-c355t-1e97b258162aa8abba70380c8f7d2ea6d44aa61f21c3f330668a3cda521e8a0f3</cites><orcidid>0000-0003-0045-2173</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12220-018-0044-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12220-018-0044-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Onnis, Irene I.</creatorcontrib><creatorcontrib>Passos Passamani, Apoena</creatorcontrib><creatorcontrib>Piu, Paola</creatorcontrib><title>Constant Angle Surfaces in Lorentzian Berger Spheres</title><title>The Journal of Geometric Analysis</title><addtitle>J Geom Anal</addtitle><description>In this work, we study helix spacelike and timelike surfaces in the Lorentzian Berger sphere
S
ε
3
, that is the three-dimensional sphere endowed with a 1-parameter family of Lorentzian metrics, obtained by deforming the round metric on
S
3
along the fibers of the Hopf fibration
S
3
→
S
2
(
1
/
2
)
by
-
ε
2
. Our main result provides a characterization of the helix surfaces in
S
ε
3
using the symmetries of the ambient space and a general helix in
S
ε
3
, with axis the infinitesimal generator of the Hopf fibers. Also, we construct some explicit examples of helix surfaces in
S
ε
3
.</description><subject>Abstract Harmonic Analysis</subject><subject>Convex and Discrete Geometry</subject><subject>Deformation</subject><subject>Differential Geometry</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Fourier Analysis</subject><subject>Geometry</subject><subject>Global Analysis and Analysis on Manifolds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1050-6926</issn><issn>1559-002X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEQhoMoWKs_wNuC562TZPOxx1r8goKHKngL0-2kbmmzNdke9NebsoInmUMm4X0mycPYNYcJBzC3iQshoARuS4CqKuGEjbhSdd6J99Pcg4JS10Kfs4uUNjmjZWVGrJp1IfUY-mIa1lsqFofosaFUtKGYd5FC_91iKO4orikWi_0HRUqX7MzjNtHV7zpmbw_3r7Oncv7y-DybzstGKtWXnGqzFMpyLRAtLpdoQFporDcrQahXVYWouRe8kV5K0NqibFaoBCeL4OWY3Qxz97H7PFDq3aY7xJCvdPmzQpq6sjqnJkNqjVtybfBdH7HJtaJd23SBfJvPpwaMlLUVKgN8AJrYpRTJu31sdxi_HAd3tOkGmy7bdEebDjIjBiblbMgu_p7yP_QDSr91lw</recordid><startdate>20190415</startdate><enddate>20190415</enddate><creator>Onnis, Irene I.</creator><creator>Passos Passamani, Apoena</creator><creator>Piu, Paola</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>IAO</scope><orcidid>https://orcid.org/0000-0003-0045-2173</orcidid></search><sort><creationdate>20190415</creationdate><title>Constant Angle Surfaces in Lorentzian Berger Spheres</title><author>Onnis, Irene I. ; Passos Passamani, Apoena ; Piu, Paola</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-1e97b258162aa8abba70380c8f7d2ea6d44aa61f21c3f330668a3cda521e8a0f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Convex and Discrete Geometry</topic><topic>Deformation</topic><topic>Differential Geometry</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Fourier Analysis</topic><topic>Geometry</topic><topic>Global Analysis and Analysis on Manifolds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Onnis, Irene I.</creatorcontrib><creatorcontrib>Passos Passamani, Apoena</creatorcontrib><creatorcontrib>Piu, Paola</creatorcontrib><collection>CrossRef</collection><collection>Gale Academic OneFile</collection><jtitle>The Journal of Geometric Analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Onnis, Irene I.</au><au>Passos Passamani, Apoena</au><au>Piu, Paola</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Constant Angle Surfaces in Lorentzian Berger Spheres</atitle><jtitle>The Journal of Geometric Analysis</jtitle><stitle>J Geom Anal</stitle><date>2019-04-15</date><risdate>2019</risdate><volume>29</volume><issue>2</issue><spage>1456</spage><epage>1478</epage><pages>1456-1478</pages><issn>1050-6926</issn><eissn>1559-002X</eissn><abstract>In this work, we study helix spacelike and timelike surfaces in the Lorentzian Berger sphere
S
ε
3
, that is the three-dimensional sphere endowed with a 1-parameter family of Lorentzian metrics, obtained by deforming the round metric on
S
3
along the fibers of the Hopf fibration
S
3
→
S
2
(
1
/
2
)
by
-
ε
2
. Our main result provides a characterization of the helix surfaces in
S
ε
3
using the symmetries of the ambient space and a general helix in
S
ε
3
, with axis the infinitesimal generator of the Hopf fibers. Also, we construct some explicit examples of helix surfaces in
S
ε
3
.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12220-018-0044-0</doi><tpages>23</tpages><orcidid>https://orcid.org/0000-0003-0045-2173</orcidid></addata></record> |
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| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Abstract Harmonic Analysis Convex and Discrete Geometry Deformation Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics |
| title | Constant Angle Surfaces in Lorentzian Berger Spheres |
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