arXiv research

Formula calculates residues for maps near holomorphic distributions.

Study on complex tori foliations and flat geometries.

Holomorphic branched Cartan geometry defined on complex manifolds.

The Wu-Yau theorem is proven for Sasakian manifolds with specific curvature conditions.

Study of flows on complex manifolds with holomorphic properties.

Establishes jet transversality for regular maps from flexible manifolds.

Study transverse $J$-holomorphic curves linking nearly Kähler $\mathbb{CP}^3$ to minimal surfaces.

Adapts Frolicher-type inequalities to foliations.

We study holomorphic foliations with an affine homogeneous transverse structure. We give a friendly characterization of the case of transversely affine foliations in terms of matrix valued pairs of differential forms. This leads naturally to the study of the case of foliations with singularities. A first extension theo…

A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.

The paper establishes Schwarz type lemmas for pseudo-Hermitian manifolds.

In this paper, we consider holomorphic mappings between real hypersurfaces in different dimensional complex spaces. We give a number of conditions that imply that such mappings are transversal to the target hypersurface at most points.

New systems derived from Hilbert schemes on surfaces.

Study of flows on 7D manifolds with holomorphic properties.

Hodge numbers of Sasakian manifolds remain unchanged under deformations.

Let F be a Kähler foliation on a compact Riemannian manifold M. we study the properties of infinitesimal automorphisms on (M,F), and in particular we concentrate on the transversal conformal field, transversal projective field and transversally holomorphic field

In this paper an analytic proof of a generalization of a theorem of Bismut ([Bis1, Theorem 5.1]) is given, which says that, when $v$ is a transversal holomorphic vector field on a compact complex manifold $X$ with a zero point set $Y$, the embedding $j:Y\to X$ induces a natural isomorphism between the holomorphic equiv…

We show that Perelman's W-functional can be generalized to Sasaki-Ricci flow. When the basic first Chern class is positive, we prove a uniform bound on the scalar curvature, the diameter and a uniform $C^1$ bound for the transverse Ricci potential along the Sasaki-Ricci flow, which generalizes Perelman's results Kahler…

Study on stability of Sasaki structures under deformations.

In this paper we study (smooth and holomorphic) foliations which are invariant under transverse actions of Lie groups.

No projective structure found on foliations of elliptic curves.

Survey on holomorphic structures on complex manifolds.

Constructs the moduli space of super J-holomorphic curves.

We study the classification of singularities of holomorphic foliations and non-integrable one-forms under the hypothesis of transversality with real hypersurfaces.

The study introduces new foliations and structures on complex manifolds.

Study deformations of Calabi-Yau foliations using Kuranishi spaces.

The paper proves conditions for the existence of holomorphic discs in Kähler manifolds.

Paper generalizes Schwarz lemma for harmonic maps between Riemannian manifolds.

Develops tools for studying intersections of elliptic operators, focusing on $J$-holomorphic maps.

In this paper, we prove that the transverse Mabuchi K-energy functional is convex along the weak geodesic in the space of Sasakian metrics. As an application, we obtain the uniqueness of constant scalar curvature Sasakian metrics modulo automorphisms for the transverse holomorphic structure.

In his 1979 paper Trotman proves, using the techniques of the Thom transversality theorem, that under some conditions on the dimensions of the manifolds under consideration, openness of the set of maps transverse to a stratification in the strong (Whitney) topology implies that the stratification is $(a)$-regular. Here…

We study blow-ups in generalized complex geometry. To that end we introduce the concept of holomorphic ideal, which allows one to define a blow-up in the category of smooth manifolds. We then investigate which generalized complex submanifolds are suitable for blowing up. Two classes naturally appear; generalized Poisso…

In this paper, we examine holomorphic Segre preserving maps between the complexifications of real hypersurfaces in $\mathbb{C}^{n+1}$. In particular, we find several sufficient conditions ensuring that Segre transversality and total Segre nondegeneracy of the maps must hold.

We describe the cohomology of a specific type of foliation on complex manifolds.

In this paper, we address a question of Donaldson's on the best estimate that can be achieved for the transversality of an asymptotically holomorphic sequence of sections of increasing powers of a line bundle over an integral symplectic manifold. More specifically, we find an upper bound for the transversality of n suc…

In this paper we give a diameter bound for Sasaki manifolds with positive transverse Ricci curvature. As an application, we obtain the uniqueness of Sasaki-Einstein metrics on compact Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure.

Study families of Lie algebroids on complex spaces, introducing unfoldings.

The paper computes a tau-invariant for holomorphic curves in Stein domains and links.

We develop some pluripotential theoretic techniques for the transversally holomorphic foliation of a Sasakian manifold. We prove the convexity of the K-energy along weak geodesics for Sasakian manifolds. This implies that the K-energy is bounded below if a constant scalar curvature structure exists with those metrics m…

We prove here new results about transversality and related geometric properties of a holomorphic, formal, or CR mapping, sending one generic submanifold of $\bC^N$ into another. One of our main results is that a finite mapping is transversal to the target manifold provided this manifold is of finite type. For the case …

Motivated by the moduli theory of taut contact circles on spherical 3-manifolds, we relate taut contact circles to transversely holomorphic flows. We give an elementary survey of such 1-dimensional foliations from a topological viewpoint. We describe a complex analogue of the classical Godbillon-Vey invariant, the so-c…

The main theorem of this paper is a result of estimated transversality with respect to stratifications of jet spaces in the approximately holomorphic category over an almost-complex manifold. The notion of asymptotic ampleness of complex vector bundles over an almost-complex manifold is also discussed, as well as appli…

Study on foliation automorphisms, finding non-Lie groups and ILH Lie groups.

Study mean curvature forms on Kähler foliations with restrictions on basic cohomology.

Deformations of the Reeb flow of a Sasakian manifold as transversely Kähler flows may not admit compatible Sasakian metrics anymore. We show that the triviality of the (0,2)-component of the basic Euler class characterizes the existence of compatible Sasakian metrics for given small deformations of the Reeb flow as tra…

Introduces positivity for $(1,1)$ classes in foliated manifolds.

We give some results concerning the smoothness of the image of a real-analytic submanifold in complex space under the action of a finite holomorphic mapping. For instance, if the submanifold is not contained in a proper complex subvariety, we give a necessary and sufficient condition guaranteeing that its image is smoo…

A generalized complex manifold which satisfies the $\partial \overline{\partial}$-lemma admits a Hodge decomposition in twisted cohomology. Using a Courant algebroid theoretic approach we study the behavior of the Hodge decomposition in smooth and holomorphic families of generalized complex manifolds. In particular we …