相关论文: Convergence of Hermitian manifolds and the Type II…

The Type IIA flow is a flow of 3-forms on a 6-dimensional symplectic manifold. It was introduced by Fei, Phong, Picard, and Zhang in \cite{FPPZb}. There is little known about the singularities of this flow in general. We formulate and prove…

We study singularity formation of K\"ahler-Ricci flow on a K\"ahler manifold that admits a horizontally homothetic conformal submersion into another K\"ahler manifold. We will derive necessary and sufficient conditions for the preservation…

We study the positive Hermitian curvature flow of left-invariant metrics on complex 2-step nilpotent Lie groups. In this setting we completely characterize the long-time behaviour of the flow, showing that normalized solutions to the flow…

We study the flow of Hermitian metrics governed by the second Chern-Ricci form on a compact complex manifolds. The flow belongs to the family of Hermitian curvature flows introduced by Streets and Tian and it was considered by Lee in order…

We write general and explicit equations which solve the supersymmetry transformations with two arbitrary complex-proportional Weyl spinors on $\mathcal{N}=1$ supersymmetric type IIB strings backgrounds with all R-R $F_1$, $F_3$, $F_5$ and…

We study the convergence of complete non-compact conformally flat solutions to the Yamabe flow to Yamabe steady solitons. We also prove the existence of Type II singularities which develop at either a finite time $T$ or as $t \to +\infty$.

It is shown that bounds of all orders of derivative would follow from uniform bounds for the metric and the torsion 1-form, for a flow in non-K\"ahler geometry which can be interpreted as either a flow for the Type IIB string or the Anomaly…

The Ricci flow was introduced by Hamilton and gained its importance through the years. Of special importance is the limiting behavior of the flow and its symmetry properties. Taking this into account, we present a novel normalization for…

We study the positive Hermitian curvature flow for left-invariant metrics on $2$-step nilpotent Lie groups with a left-invariant complex structure $J$. We describe the long-time behavior of the flow under the assumption that…

We study the positive Hermitian curvature flow on the space of left-invariant metrics on complex Lie groups. We show that in the nilpotent case, the flow exists for all positive times and subconverges in the Cheeger-Gromov sense to a…

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 flows in symplectic geometry and flows in…

We study type IIB supergravity solutions with four supersymmetries that interpolate between two types widely considered in the literature: the dual of Becker and Becker's compactifications of M-theory to 3 dimensions and the dual of…

We study a family of fermionic extensions of the Camassa-Holm equation. Within this family we identify three interesting classes: (a) equations, which are inherently hamiltonian, describing geodesic flow with respect to an H^1 metric on the…

We contribute to an original problem studied by Hamilton and others, in order to understand the behaviour of maximal solutions of the Ricci flow both in compact and non-compact complete orientable Riemannian manifolds of finite volume. The…

A fundamental tool in the analysis of Ricci flow is a compactness result of Hamilton in the spirit of the work of Cheeger, Gromov and others. Roughly speaking it allows one to take a sequence of Ricci flows with uniformly bounded curvature…

We study the gradient flow of the $L^2-$norm of the second fundamental form of smooth immersions of two-dimensional surfaces into compact Riemannian manifolds. By analogy with the results obtained for the Willmore flow in Riemannian…

We consider the existence of cohomogeneity one solitons for the isometric flow of $G_2$-structures on the following classes of torsion-free $G_2$-manifolds: the Euclidean $R^7$ with its standard $G_2$-structure, metric cylinders over…

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) holonomy, but with respect to the projected…

In this work, we first establish short time existence and Shi's type estimate of second Ricci flow on complete noncompact Hermitian manifolds. As an application, we use the second Ricci flow to discuss the existence of Kaehler-Einstein…

We study the asymptotic behavior of the pluriclosed flow in the case of left-invariant Hermitian structures on Lie groups. We prove that solutions on 2-step nilpotent Lie groups and on almost-abelian Lie groups converge, after a suitable…