• Corpus ID: 227254007

Bochner-Kodaira Formulas and the Type IIA Flow

@article{Fei2020BochnerKodairaFA,
  title={Bochner-Kodaira Formulas and the Type IIA Flow},
  author={Teng Fei and Duong Hong Phong and S{\'e}bastien Picard and Xiangwen Zhang},
  journal={arXiv: Differential Geometry},
  year={2020}
}
A new derivation of the flow of metrics in the Type IIA flow is given. It is adapted to the formulation of the flow as a variant of a Laplacian flow, and it uses the projected Levi-Civita connection of the metrics themselves instead of their conformal rescalings. 
View PDF on arXiv
3 Citations
Background Citations
2
Methods Citations
1

3 Citations

Stability of the Type IIA flow and its applications in symplectic geometry
In this paper the dynamical stability of the Type IIA flow with no source near its stationary points is established. These stationary points had been shown previously by the authors to be Ricci-flat…
Special solutions to the Type IIA flow
We consider the source-free Type IIA flow introduced by Fei-Phong-PicardZhang [10], and we study it in the case when the relevant geometric datum is a symplectic half-flat SU(3)-structure. We show…
Symplectic geometric flows
Several geometric flows on symplectic manifolds are introduced which are potentially of interest in symplectic geometry and topology. They are motivated by the Type IIA flow and T-duality between…

References

SHOWING 1-10 OF 34 REFERENCES
The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation
The purpose of this paper is to solve a problem posed by Strominger in constructing smooth models of superstring theory with flux. These are given by non-Kahler manifolds with torsion.
Geometric flows for the Type IIA string
A geometric flow on $6$-dimensional symplectic manifolds is introduced which is motivated by supersymmetric compactifications of the Type IIA string. The underlying structure turns out to be SU(3)…
Reformulating supersymmetry with a generalized Dolbeault operator
The conditions for = 1 supersymmetry in type II supergravity have been previously reformulated in terms of generalized complex geometry. We improve that reformulation so as to completely eliminate…
Generalized Cohomologies and Supersymmetry
We show that the complex cohomologies of Bott, Chern, and Aeppli and the symplectic cohomologies of Tseng and Yau arise in the context of type II string theory. Specifically, they can be used to…
Generalized structures of N=1 vacua
We characterize = 1 vacua of type-II theories in terms of generalized complex structure on the internal manifold M. The structure group of T(M)⊕T*(M) being SU(3) × SU(3) implies the existence of two…
THE GEOMETRY OF THREE-FORMS IN SIX DIMENSIONS
We study the special algebraic properties of alternating 3-forms in 6 dimensions and introduce a diffeomorphism-invariant functional on the space of differential 3-forms on a closed 6-manifold M .…
A Monge?Ampère-type equation motivated by string theory
There is a rich class of non-Kähler complex manifolds for dimension greater than two. It is therefore important to construct canonical geometry on such manifolds. Since non-Kähler geometry is not as…
Some remarks on G2-structures
This article consists of loosely related remarks about the geometry of G2structures on 7-manifolds, some of which are based on unpublished joint work with two other people: F. Reese Harvey and Steven…
Laplacian Flow of Closed G$$_2$$2-Structures Inducing Nilsolitons
We study the existence of left invariant closed $$G_2$$G2-structures defining a Ricci soliton metric on simply connected nonabelian nilpotent Lie groups. For each one of these $$G_2$$G2-structures,…
The Fu–Yau equation with negative slope parameter
The Fu–Yau equation is an equation introduced by Fu and Yau as a generalization to arbitrary dimensions of an ansatz for the Strominger system. As in the Strominger system, it depends on a slope…
...
...