On a class of almost Kenmotsu manifolds admitting an Einstein like structure
In the present paper, we introduce the notion of ∗ -gradient ρ -Einstein soliton on a class of almost Kenmotsu manifolds. It is shown that if a ( 2 n + 1 ) -dimensional ( k , μ ) ′ -almost Kenmotsu manifold M admits ∗ -gradient ρ -Einstein soliton with Einstein potential f , then (1) the manifold M...
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| Veröffentlicht in: | São Paulo Journal of Mathematical Sciences 2021-06, Vol.15 (1), p.335-343 |
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| container_title | São Paulo Journal of Mathematical Sciences |
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| creator | Dey, Dibakar Majhi, Pradip |
| description | In the present paper, we introduce the notion of
∗
-gradient
ρ
-Einstein soliton on a class of almost Kenmotsu manifolds. It is shown that if a
(
2
n
+
1
)
-dimensional
(
k
,
μ
)
′
-almost Kenmotsu manifold
M
admits
∗
-gradient
ρ
-Einstein soliton with Einstein potential
f
, then (1) the manifold
M
is locally isometric to
H
n
+
1
(
-
4
)
×
R
n
, (2) the manifold
M
is
∗
-Ricci flat and (3) the Einstein potential
f
is harmonic or satisfies a physical Poisson’s equation. Finally, an illustrative example is presented. |
| doi_str_mv | 10.1007/s40863-021-00228-1 |
| format | Article |
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∗
-gradient
ρ
-Einstein soliton on a class of almost Kenmotsu manifolds. It is shown that if a
(
2
n
+
1
)
-dimensional
(
k
,
μ
)
′
-almost Kenmotsu manifold
M
admits
∗
-gradient
ρ
-Einstein soliton with Einstein potential
f
, then (1) the manifold
M
is locally isometric to
H
n
+
1
(
-
4
)
×
R
n
, (2) the manifold
M
is
∗
-Ricci flat and (3) the Einstein potential
f
is harmonic or satisfies a physical Poisson’s equation. Finally, an illustrative example is presented.</description><identifier>ISSN: 1982-6907</identifier><identifier>EISSN: 2316-9028</identifier><identifier>EISSN: 2306-9028</identifier><identifier>DOI: 10.1007/s40863-021-00228-1</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Mathematics ; Mathematics and Statistics ; Original Article ; Solitary waves</subject><ispartof>São Paulo Journal of Mathematical Sciences, 2021-06, Vol.15 (1), p.335-343</ispartof><rights>Instituto de Matemática e Estatística da Universidade de São Paulo 2021</rights><rights>Instituto de Matemática e Estatística da Universidade de São Paulo 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-4a90010aa1e7d3d3169e5a2059f66d68bec7141d51b1ef9dc61e968e0c584ab23</citedby><cites>FETCH-LOGICAL-c319t-4a90010aa1e7d3d3169e5a2059f66d68bec7141d51b1ef9dc61e968e0c584ab23</cites><orcidid>0000-0001-8992-6501</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/s40863-021-00228-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40863-021-00228-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Dey, Dibakar</creatorcontrib><creatorcontrib>Majhi, Pradip</creatorcontrib><title>On a class of almost Kenmotsu manifolds admitting an Einstein like structure</title><title>São Paulo Journal of Mathematical Sciences</title><addtitle>São Paulo J. Math. Sci</addtitle><description>In the present paper, we introduce the notion of
∗
-gradient
ρ
-Einstein soliton on a class of almost Kenmotsu manifolds. It is shown that if a
(
2
n
+
1
)
-dimensional
(
k
,
μ
)
′
-almost Kenmotsu manifold
M
admits
∗
-gradient
ρ
-Einstein soliton with Einstein potential
f
, then (1) the manifold
M
is locally isometric to
H
n
+
1
(
-
4
)
×
R
n
, (2) the manifold
M
is
∗
-Ricci flat and (3) the Einstein potential
f
is harmonic or satisfies a physical Poisson’s equation. Finally, an illustrative example is presented.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Article</subject><subject>Solitary waves</subject><issn>1982-6907</issn><issn>2316-9028</issn><issn>2306-9028</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAQhi0EElXpH2CyxGy4c2LHHlFVPkSlLjBbbuJUKYldbGfg3xMIEhu33PI-750eQq4RbhGgukslKFkw4MgAOFcMz8iCFyiZBq7OyQK14kxqqC7JKqUjTCPKSgtYkO3OU0vr3qZEQ0ttP4SU6YvzQ8hppIP1XRv6JlHbDF3OnT9Q6-mm8ym7ztO-e3c05TjWeYzuily0tk9u9buX5O1h87p-Ytvd4_P6fsvqAnVmpdUACNaiq5qimR7VTlgOQrdSNlLtXV1hiY3APbpWN7VEp6VyUAtV2j0vluRm7j3F8DG6lM0xjNFPJw0XXKpSFFJPKT6n6hhSiq41p9gNNn4aBPMtzszizCTO_IgzOEHFDKUp7A8u_lX_Q30BqM5v6g</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>Dey, Dibakar</creator><creator>Majhi, Pradip</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-8992-6501</orcidid></search><sort><creationdate>20210601</creationdate><title>On a class of almost Kenmotsu manifolds admitting an Einstein like structure</title><author>Dey, Dibakar ; Majhi, Pradip</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-4a90010aa1e7d3d3169e5a2059f66d68bec7141d51b1ef9dc61e968e0c584ab23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Article</topic><topic>Solitary waves</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dey, Dibakar</creatorcontrib><creatorcontrib>Majhi, Pradip</creatorcontrib><collection>CrossRef</collection><jtitle>São Paulo Journal of Mathematical Sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dey, Dibakar</au><au>Majhi, Pradip</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On a class of almost Kenmotsu manifolds admitting an Einstein like structure</atitle><jtitle>São Paulo Journal of Mathematical Sciences</jtitle><stitle>São Paulo J. Math. Sci</stitle><date>2021-06-01</date><risdate>2021</risdate><volume>15</volume><issue>1</issue><spage>335</spage><epage>343</epage><pages>335-343</pages><issn>1982-6907</issn><eissn>2316-9028</eissn><eissn>2306-9028</eissn><abstract>In the present paper, we introduce the notion of
∗
-gradient
ρ
-Einstein soliton on a class of almost Kenmotsu manifolds. It is shown that if a
(
2
n
+
1
)
-dimensional
(
k
,
μ
)
′
-almost Kenmotsu manifold
M
admits
∗
-gradient
ρ
-Einstein soliton with Einstein potential
f
, then (1) the manifold
M
is locally isometric to
H
n
+
1
(
-
4
)
×
R
n
, (2) the manifold
M
is
∗
-Ricci flat and (3) the Einstein potential
f
is harmonic or satisfies a physical Poisson’s equation. Finally, an illustrative example is presented.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s40863-021-00228-1</doi><tpages>9</tpages><orcidid>https://orcid.org/0000-0001-8992-6501</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1982-6907 |
| ispartof | São Paulo Journal of Mathematical Sciences, 2021-06, Vol.15 (1), p.335-343 |
| issn | 1982-6907 2316-9028 2306-9028 |
| language | eng |
| recordid | cdi_proquest_journals_2526845369 |
| source | SpringerNature Journals |
| subjects | Mathematics Mathematics and Statistics Original Article Solitary waves |
| title | On a class of almost Kenmotsu manifolds admitting an Einstein like structure |
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