L1-2-Type Surfaces in 3-Dimensional De Sitter and Anti De Sitter Spaces
Let M s 2 be an orientable surface immersed in the De Sitter space S 1 3 ⊂ R 1 4 or anti de Sitter space H 1 3 ⊂ R 2 4 . In the case that M s 2 is of L 1 -2-type we prove that the following conditions are equivalent to each other: M s 2 has a constant principal curvature; M s 2 has constant mean cur...
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2023, Vol.46 (4) |
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| creator | García-Martínez, S. Carolina Lucas, Pascual Ramírez-Ospina, H. Fabián |
| description | Let
M
s
2
be an orientable surface immersed in the De Sitter space
S
1
3
⊂
R
1
4
or anti de Sitter space
H
1
3
⊂
R
2
4
. In the case that
M
s
2
is of
L
1
-2-type we prove that the following conditions are equivalent to each other:
M
s
2
has a constant principal curvature;
M
s
2
has constant mean curvature;
M
s
2
has constant second mean curvature. As a consequence, we also show that an
L
1
-2-type surface is either an open portion of a standard pseudo-Riemannian product, or a
B
-scroll over a null curve, or else its mean curvature, its Gaussian curvature and its principal curvatures are all non-constant. |
| doi_str_mv | 10.1007/s40840-023-01535-w |
| format | Article |
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M
s
2
be an orientable surface immersed in the De Sitter space
S
1
3
⊂
R
1
4
or anti de Sitter space
H
1
3
⊂
R
2
4
. In the case that
M
s
2
is of
L
1
-2-type we prove that the following conditions are equivalent to each other:
M
s
2
has a constant principal curvature;
M
s
2
has constant mean curvature;
M
s
2
has constant second mean curvature. As a consequence, we also show that an
L
1
-2-type surface is either an open portion of a standard pseudo-Riemannian product, or a
B
-scroll over a null curve, or else its mean curvature, its Gaussian curvature and its principal curvatures are all non-constant.</description><identifier>ISSN: 0126-6705</identifier><identifier>EISSN: 2180-4206</identifier><identifier>DOI: 10.1007/s40840-023-01535-w</identifier><language>eng</language><publisher>Singapore: Springer Nature Singapore</publisher><subject>Applications of Mathematics ; Curvature ; Mathematics ; Mathematics and Statistics</subject><ispartof>Bulletin of the Malaysian Mathematical Sciences Society, 2023, Vol.46 (4)</ispartof><rights>The Author(s) 2023</rights><rights>The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000-0002-4354-9736</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/s40840-023-01535-w$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40840-023-01535-w$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>García-Martínez, S. Carolina</creatorcontrib><creatorcontrib>Lucas, Pascual</creatorcontrib><creatorcontrib>Ramírez-Ospina, H. Fabián</creatorcontrib><title>L1-2-Type Surfaces in 3-Dimensional De Sitter and Anti De Sitter Spaces</title><title>Bulletin of the Malaysian Mathematical Sciences Society</title><addtitle>Bull. Malays. Math. Sci. Soc</addtitle><description>Let
M
s
2
be an orientable surface immersed in the De Sitter space
S
1
3
⊂
R
1
4
or anti de Sitter space
H
1
3
⊂
R
2
4
. In the case that
M
s
2
is of
L
1
-2-type we prove that the following conditions are equivalent to each other:
M
s
2
has a constant principal curvature;
M
s
2
has constant mean curvature;
M
s
2
has constant second mean curvature. As a consequence, we also show that an
L
1
-2-type surface is either an open portion of a standard pseudo-Riemannian product, or a
B
-scroll over a null curve, or else its mean curvature, its Gaussian curvature and its principal curvatures are all non-constant.</description><subject>Applications of Mathematics</subject><subject>Curvature</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0126-6705</issn><issn>2180-4206</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNpNkE1Lw0AQhhdRMNT-AU8Lnldn9ivbY2m1CgEPreclH7uSUpO4mxD896ZG0LkMzPvMMDyE3CLcI0D6ECUYCQy4YIBKKDZekISjASY56EuSAHLNdArqmixjPMJUSnPNMSG7DBlnh6_O0f0QfF66SOuGCratP1wT67bJT3Q7hXXfu0DzpqLrpq__jfbdeemGXPn8FN3yty_I29PjYfPMstfdy2adsQ4lH5lAVZgSjajQeYCqLFXhVJrmHHxRpbzQuTep8VJ66XWhy5V36JTXGoVCrcWC3M13u9B-Di729tgOYXoyWm64MmK1AjVRYqZiF-rm3YU_CsGepdlZmp2k2R9pdhTfJlNdKQ</recordid><startdate>2023</startdate><enddate>2023</enddate><creator>García-Martínez, S. Carolina</creator><creator>Lucas, Pascual</creator><creator>Ramírez-Ospina, H. Fabián</creator><general>Springer Nature Singapore</general><general>Springer Nature B.V</general><scope>C6C</scope><orcidid>https://orcid.org/0000-0002-4354-9736</orcidid></search><sort><creationdate>2023</creationdate><title>L1-2-Type Surfaces in 3-Dimensional De Sitter and Anti De Sitter Spaces</title><author>García-Martínez, S. Carolina ; Lucas, Pascual ; Ramírez-Ospina, H. Fabián</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p142w-315b8c183d1ef00dcc5be577a20fbd72b6af878f44f4f6b6c9fe1e5f661351663</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Applications of Mathematics</topic><topic>Curvature</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>García-Martínez, S. Carolina</creatorcontrib><creatorcontrib>Lucas, Pascual</creatorcontrib><creatorcontrib>Ramírez-Ospina, H. Fabián</creatorcontrib><collection>Springer Nature OA Free Journals</collection><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>García-Martínez, S. Carolina</au><au>Lucas, Pascual</au><au>Ramírez-Ospina, H. Fabián</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>L1-2-Type Surfaces in 3-Dimensional De Sitter and Anti De Sitter Spaces</atitle><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle><stitle>Bull. Malays. Math. Sci. Soc</stitle><date>2023</date><risdate>2023</risdate><volume>46</volume><issue>4</issue><issn>0126-6705</issn><eissn>2180-4206</eissn><abstract>Let
M
s
2
be an orientable surface immersed in the De Sitter space
S
1
3
⊂
R
1
4
or anti de Sitter space
H
1
3
⊂
R
2
4
. In the case that
M
s
2
is of
L
1
-2-type we prove that the following conditions are equivalent to each other:
M
s
2
has a constant principal curvature;
M
s
2
has constant mean curvature;
M
s
2
has constant second mean curvature. As a consequence, we also show that an
L
1
-2-type surface is either an open portion of a standard pseudo-Riemannian product, or a
B
-scroll over a null curve, or else its mean curvature, its Gaussian curvature and its principal curvatures are all non-constant.</abstract><cop>Singapore</cop><pub>Springer Nature Singapore</pub><doi>10.1007/s40840-023-01535-w</doi><orcidid>https://orcid.org/0000-0002-4354-9736</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0126-6705 |
| ispartof | Bulletin of the Malaysian Mathematical Sciences Society, 2023, Vol.46 (4) |
| issn | 0126-6705 2180-4206 |
| language | eng |
| recordid | cdi_proquest_journals_2825839905 |
| source | SpringerLink Journals |
| subjects | Applications of Mathematics Curvature Mathematics Mathematics and Statistics |
| title | L1-2-Type Surfaces in 3-Dimensional De Sitter and Anti De Sitter Spaces |
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