Pseudo-Kähler Geometry of Properly Convex Projective Structures on the torus
In this paper we prove the existence of a pseudo-Kähler structure on the deformation space B 0 ( T 2 ) of properly convex R P 2 -structures over the torus. In particular, the pseudo-Riemannian metric and the symplectic form are compatible with the complex structure inherited from the identification...
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| Veröffentlicht in: | The Journal of geometric analysis 2024-04, Vol.34 (4), Article 116 |
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| container_title | The Journal of geometric analysis |
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| creator | Rungi, Nicholas Tamburelli, Andrea |
| description | In this paper we prove the existence of a pseudo-Kähler structure on the deformation space
B
0
(
T
2
)
of properly convex
R
P
2
-structures over the torus. In particular, the pseudo-Riemannian metric and the symplectic form are compatible with the complex structure inherited from the identification of
B
0
(
T
2
)
with the complement of the zero section of the total space of the bundle of cubic holomorphic differentials over the Teichmüller space. We show that the
S
1
-action on
B
0
(
T
2
)
, given by rotation of the fibers, is Hamiltonian and it preserves both the metric and the symplectic form. Finally, we prove the existence of a moment map for the
SL
(
2
,
R
)
-action over
B
0
(
T
2
)
. |
| doi_str_mv | 10.1007/s12220-023-01491-8 |
| format | Article |
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B
0
(
T
2
)
of properly convex
R
P
2
-structures over the torus. In particular, the pseudo-Riemannian metric and the symplectic form are compatible with the complex structure inherited from the identification of
B
0
(
T
2
)
with the complement of the zero section of the total space of the bundle of cubic holomorphic differentials over the Teichmüller space. We show that the
S
1
-action on
B
0
(
T
2
)
, given by rotation of the fibers, is Hamiltonian and it preserves both the metric and the symplectic form. Finally, we prove the existence of a moment map for the
SL
(
2
,
R
)
-action over
B
0
(
T
2
)
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B
0
(
T
2
)
of properly convex
R
P
2
-structures over the torus. In particular, the pseudo-Riemannian metric and the symplectic form are compatible with the complex structure inherited from the identification of
B
0
(
T
2
)
with the complement of the zero section of the total space of the bundle of cubic holomorphic differentials over the Teichmüller space. We show that the
S
1
-action on
B
0
(
T
2
)
, given by rotation of the fibers, is Hamiltonian and it preserves both the metric and the symplectic form. Finally, we prove the existence of a moment map for the
SL
(
2
,
R
)
-action over
B
0
(
T
2
)
.</description><subject>Abstract Harmonic Analysis</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Fourier Analysis</subject><subject>Global Analysis and Analysis on Manifolds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Toruses</subject><issn>1050-6926</issn><issn>1559-002X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kM9KAzEQh4MoWKsv4CngOTr5s5vkKEWrWFFQwVvY7s7alnZTk2yx7-Ob-GJuXcGbp5mB7_cb-Ag55XDOAfRF5EIIYCAkA64sZ2aPDHiWWQYgXve7HTJguRX5ITmKcQGgcqn0gNw_Rmwrz-6-PmdLDHSMfoUpbKmv6WPwawzLLR35ZoMfu3uBZZpvkD6l0JapDRipb2iaIU0-tPGYHNTFMuLJ7xySl-ur59ENmzyMb0eXE1YKDYkpW6iCl9VUmBzqClAYJa3QSmEpudU1t1mGBjLFeTatuDXG6LqQHAzPFSg5JGd97zr49xZjcgvfhqZ76YSV0oABbTpK9FQZfIwBa7cO81URto6D22lzvTbXaXM_2twuJPtQ7ODmDcNf9T-pb6xSbzw</recordid><startdate>20240401</startdate><enddate>20240401</enddate><creator>Rungi, Nicholas</creator><creator>Tamburelli, Andrea</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-4799-9213</orcidid></search><sort><creationdate>20240401</creationdate><title>Pseudo-Kähler Geometry of Properly Convex Projective Structures on the torus</title><author>Rungi, Nicholas ; Tamburelli, Andrea</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-49a4a1cdb2860fd0e284392744ec3197f1955e8054115bd198887fa3108164043</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Fourier Analysis</topic><topic>Global Analysis and Analysis on Manifolds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Toruses</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rungi, Nicholas</creatorcontrib><creatorcontrib>Tamburelli, Andrea</creatorcontrib><collection>CrossRef</collection><jtitle>The Journal of geometric analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Rungi, Nicholas</au><au>Tamburelli, Andrea</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Pseudo-Kähler Geometry of Properly Convex Projective Structures on the torus</atitle><jtitle>The Journal of geometric analysis</jtitle><stitle>J Geom Anal</stitle><date>2024-04-01</date><risdate>2024</risdate><volume>34</volume><issue>4</issue><artnum>116</artnum><issn>1050-6926</issn><eissn>1559-002X</eissn><abstract>In this paper we prove the existence of a pseudo-Kähler structure on the deformation space
B
0
(
T
2
)
of properly convex
R
P
2
-structures over the torus. In particular, the pseudo-Riemannian metric and the symplectic form are compatible with the complex structure inherited from the identification of
B
0
(
T
2
)
with the complement of the zero section of the total space of the bundle of cubic holomorphic differentials over the Teichmüller space. We show that the
S
1
-action on
B
0
(
T
2
)
, given by rotation of the fibers, is Hamiltonian and it preserves both the metric and the symplectic form. Finally, we prove the existence of a moment map for the
SL
(
2
,
R
)
-action over
B
0
(
T
2
)
.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12220-023-01491-8</doi><orcidid>https://orcid.org/0000-0003-4799-9213</orcidid></addata></record> |
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| ispartof | The Journal of geometric analysis, 2024-04, Vol.34 (4), Article 116 |
| issn | 1050-6926 1559-002X |
| language | eng |
| recordid | cdi_proquest_journals_2933808078 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics Toruses |
| title | Pseudo-Kähler Geometry of Properly Convex Projective Structures on the torus |
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