arXiv subjects
Publications and source records attributed to Teng Fei.
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 complex geometry. Examples include the Hitchin gradient flow on symplectic manifolds, and a new flow which is called the dual Ricci flow.
As subjective artistic creations, artistic paintings carry emotion of their creators. Emotions expressed in paintings and emotion aroused in spectators by paintings are two kinds of emotions that scholars have paid attention to. Traditional studies on emotions expressed by paintings are mainly conducted from qualitative perspectives, with neither quantitative output on the emotional values of a painting, nor exploration of trends in the expression of emotion in art history. In this research we threat facial expressions in paintings as an artistic characteristics of art history and employ cognitive computation technology to identify the facial emotions in paintings and to investigate the quantitative measures of paintings from three emotion-related aspects: the spatial and temporal patterns of painting emotions in art history, the gender difference on the emotion of paintings and the color preference associated with emotions. We discovered that the emotion of happiness has a growing trend from ancient to modern times in paintings history, and men and women have different facial expressions patterns along time. As for color preference, artists with different culture backgrounds had similar association preferences between colors and emotions.
In this paper we construct explicit smooth solutions to the Strominger system on generalized Calabi-Gray manifolds, which are compact non-Kähler Calabi-Yau 3-folds with infinitely many distinct topological types and sets of Hodge numbers.
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.
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 Levi-Civita connection of an almost-Hermitian structure. The short-time existence is established, and new identities for the Nijenhuis tensor are found which are crucial for Shi-type estimates. The integrable case can be completely solved, giving an alternative proof of Yau's theorem on Ricci-flat Kähler metrics. In the non-integrable case, models are worked out which suggest that the flow should lead to optimal almost-complex structures compatible with the given symplectic form.
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-Kähler geometry which can be interpreted as either a flow for the Type IIB string or the Anomaly flow with source term and zero slope parameter. A key ingredient in the proof is a formulation of this flow unifying it with the Ricci flow, which was recently found.
A new formulation of the Anomaly flow in the case of vanishing slope parameter is given, where the dependence on the global section of the canonical bundle appears only in the initial data. This allows a natural unification of the Anomaly flow with the Kähler-Ricci flow.
The emergence of big data enables us to evaluate the various human emotions at places from a statistic perspective by applying affective computing. In this study, a novel framework for extracting human emotions from large-scale georeferenced photos at different places is proposed. After the construction of places based on spatial clustering of user generated footprints collected in social media websites, online cognitive services are utilized to extract human emotions from facial expressions using the state-of-the-art computer vision techniques. And two happiness metrics are defined for measuring the human emotions at different places. To validate the feasibility of the framework, we take 80 tourist attractions around the world as an example and a happiness ranking list of places is generated based on human emotions calculated over 2 million faces detected out from over 6 million photos. Different kinds of geographical contexts are taken into consideration to find out the relationship between human emotions and environmental factors. Results show that much of the emotional variation at different places can be explained by a few factors such as openness. The research may offer insights on integrating human emotions to enrich the understanding of sense of place in geography and in place-based GIS.
In this paper, we study the dual Anomaly flow, which is a dual version of the Anomaly flow under T-duality. A family of monotone functionals is introduced and used to estimate the dilaton function along the flow. Many examples and reductions of the dual Anomaly flow are worked out in detail.
We give an expository about compactification of heteorotic superstrings with torsion on generalized Calabi-Gray manifolds.
A one-parameter family of coupled flows depending on a parameter $κ>0$ is introduced which reduces when $κ=1$ to the coupled flow of a metric $ω$ with a $(1,1)$-form $α$ due recently to Y. Li, Y. Yuan, and Y. Zhang. It is shown in particular that, for $κ\not=1$, estimates for derivatives of all orders would follow from $C^0$ estimates for $ω$ and $α$. Together with the monotonicity of suitably adapted energy functionals, this can be applied to establish the convergence of the flow in some situations, including on Riemann surfaces. Very little is known as yet about the monotonicity and convergence of flows in presence of couplings, and conditions such as $κ\not=1$ seem new and may be useful in the future.
Ansatze are constructed under which the solutions of 11D supergravity must be stationary points of a parabolic flow on a Riemannian manifold $M^{10-p}$. This parabolic flow turns out to be the Ricci flow coupled to a scalar field, a $(3-p)$-form, and a $4$-form. This allows the introduction of techniques from parabolic partial differential equations to the search of solutions to 11D supergravity. As a first step, Shi-type estimates and criteria for the long-time existence of the flow are established.
Necessary and sufficient conditions are provided for a class of warped product manifolds with non-vanishing flux to be supersymmetric solutions of 11D supergravity. Many noncompact, but complete solutions can be obtained in this manner, including the multi-membrane solution initially found by Duff and Stelle. In a different direction, an explicit 5-parameter moduli space of solutions to 11D supergravity is also constructed which can be viewed as nonsupersymmetric deformations of the Duff-Stelle solution.
We initiate the study of a new nonlinear parabolic equation on a Riemann surface. The evolution equation arises as a reduction of the Anomaly flow on a fibration. We obtain a criterion for long-time existence for this flow, and give a range of initial data where a singularity forms in finite time, as well as a range of initial data where the solution exists for all time. A geometric interpretation of these results is given in terms of the Anomaly flow on a Calabi-Yau threefold.
Based on the work of Schoen-Yau, we derive an estimate of the first eigenvalue of a Schrödinger Operator (the Jaocbi operator of minimal surfaces in flat 3-spaces) on surfaces.
We propose a new construction of compact non-Kähler Calabi-Yau manifolds with balanced metrics and study the Strominger system on them. In particular, we obtain explicit solutions to the Strominger system with degeneracies on $Σ_g\times T^4$, where $Σ_g$ is an immersed minimal surface of genus $g\geq3$ in $T^3$.
We construct solutions to the Strominger system on a class of noncompact Calabi-Yau 3-folds. These spaces include $\mathbb{C}^3$ and resolved conifold $\mathcal{O}(-1,-1)$ as special examples.
The connection between Hitchin's stable forms and vector cross products is observed. Using this correspondence, we construct new examples of non-Kahler Calabi-Yau 3-folds and manifolds with G2-structure of class W3. We also generalize and refine results of Calabi and Gray in the paracomplex setting.