Vaisman Metrics and the Pluriclosed Flow

Authors

Eduardo Perez, Florida International UniversityFollow

Document Type

Dissertation

Degree

Doctor of Philosophy (PhD)

Major/Program

Mathematical Sciences

First Advisor's Name

Gueo Grantcharov

First Advisor's Committee Title

Co-committee chair

Second Advisor's Name

Anna Maria Fino

Second Advisor's Committee Title

Co-committee chair

Third Advisor's Name

Bao Qin Li

Third Advisor's Committee Title

Committee member

Fourth Advisor's Name

Mirroslav Yotov

Fourth Advisor's Committee Title

Committee member

Fifth Advisor's Name

Misak Sargsian

Fifth Advisor's Committee Title

Committee member

Keywords

Ricci, flow, pluriclosed, Vaisman, invariant, metric, Kodaira

Date of Defense

6-27-2024

Abstract

In this thesis we study T²-invariant pluriclosed metrics on the Kodaira-Thurston surface, we obtain a characterization of T²-invariant Vaisman metrics, and notice that the Kodaira-Thurston surface admits Vaisman metrics whose Ricci scalars are not constant. We then study the behaviour of the Vaisman condition in correspondence with the pluriclosed flow. As a corollary, we prove that the Vaisman condition is preserved by the pluriclosed flow if and only if the Ricci scalar of the initial T²-invariant metric is constant. We also explore metrics on primary Hopf surface of class 1, which also preserve the Vaisman condition. Lastly, as part of ongoing research, we study how these metrics of the Hopf surface evolve under the pluriclosed flow.

Identifier

FIDC011224

Comments

A portion of this dissertation contains joint work with Dr. Anna Maria Fino and Dr. Gueo Grantcharov.

Previously Published In

A. Fino, G. Grantcharov, E. Perez, The Pluriclosed Flow For T 2 -Invariant Vaisman Metrics On The Kodaira-Thurston Surface. J. Geom. Phys. 201 (2024), Paper No. 105197, 10 pp.

Recommended Citation

Perez, Eduardo, "Vaisman Metrics and the Pluriclosed Flow" (2024). FIU Electronic Theses and Dissertations. 5348.
https://digitalcommons.fiu.edu/etd/5348