scholarly journals The Kähler-Ricci flow, holomorphic vector fields and Fano bundles

2021 ◽  
pp. 1
Author(s):  
Xi Sisi Shen
Keyword(s):  
Ricci Flow ◽  
Vector Fields ◽  
Holomorphic Vector Fields

Sasaki–Ricci flow on Sasaki–Einstein space T1,1 and deformations

2018 ◽  
Vol 33 (34) ◽  
pp. 1845014 ◽  
Author(s):  
Mihai Visinescu
Keyword(s):  
Ricci Flow ◽  
Vector Fields ◽  
Hamiltonian Function ◽  
Ricci Soliton ◽  
Einstein Space ◽  
Reeb Vector ◽  
Kähler Structure ◽  
Reeb Vector Field ◽  
Holomorphic Vector Fields ◽  
Kähler Potential

We study the transverse Kähler structure of the Sasaki–Einstein space [Formula: see text]. A set of local holomorphic coordinates is introduced and a Sasakian analogue of the Kähler potential is given. We investigate deformations of the Sasaki–Einstein structure preserving the Reeb vector field, but modifying the contact form. For this kind of deformations, we consider the Sasaki–Ricci flow which converges in a suitable sense to a Sasaki–Ricci soliton. Finally, it is described the constructions of Hamiltonian holomorphic vector fields and Hamiltonian function on the [Formula: see text] manifold.

Holomorphic vector fields with simple isolated zeros

1974 ◽  
Vol 208 (2) ◽  
pp. 171-173 ◽  
Author(s):  
Czes Kosniowski
Keyword(s):  
Vector Fields ◽  
Holomorphic Vector Fields

scholarly journals Functions Holomorphic along Holomorphic Vector Fields

2009 ◽  
Vol 19 (3) ◽  
pp. 655-666 ◽  
Author(s):  
Kang-Tae Kim ◽  
Evgeny Poletsky ◽  
Gerd Schmalz
Keyword(s):  
Vector Fields ◽  
Holomorphic Vector Fields
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