arXiv research

Compact complex manifolds with specific group actions are conformally flat.

Study on holomorphic discs in bundles over compact surfaces, proving Fredholm regularity under certain conditions.

We classify the transitive, effective, holomorphic actions of connected complex Lie groups on complex surfaces.

If $X$ is a connected complex manifold with $d_X = 2$ that admits the holomorphic and transitive action of a (connected) Lie group $G$, then the action extends to an action of the complexification $\hat{G}$ of $G$ on $X$ except when either the unit disk or else a strictly pseudoconcave homogeneous complex manifold is i…

Study optimal holomorphic extensions on complex manifolds with transitivity property.

Let $X$ be a differentiable manifold endowed with a transitive action $α:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: {enumerate} equ…

Holomorphic actions on complex spaces for nilpotent groups.

We show that holomorphic riemannian metrics on compact complex threefolds are locally homogeneous (the pseudogroup of local isometries acts transitively on the manifold).

We classify all holomorphic actions of higher rank lattices on compact Kaehler manifolds of dimension 3. This provides a complete answer to Zimmer's program for holomorphic actions on compact Kaehler manifolds of dimension at most 3.

We consider principal fibre bundles with a given connection and construct almost complex structures on the total space if the adjoint bundle is isomorphic to the tangent bundle of the base. We derive the integrability condition. If the structure group is compact, then a choice of an ad-invariant inner product on its Li…

Study non-transitive pseudo-Anosov flows using group actions.

Constructs special Lagrangian 3-spheres in non-Kähler compact threefolds.

We introduce a natural generalisation of holomorphic curves to morphisms of supermanifolds, referred to as holomorphic supercurves. More precisely, supercurves are morphisms from a Riemann surface, endowed with the structure of a supermanifold which is induced by a holomorphic line bundle, to an ordinary almost complex…

Study of isometries on hyperbolic 3-manifold cusps.

Study of flows on complex manifolds with holomorphic properties.

Study groups acting on trees with specific local actions, proving cohomology vanishing or infinite.

This paper studies actions of solvable Lie groups on nilpotent Lie groups.

A transitive smooth action of a connected Lie group G on a manifold M is called almost primitive (resp. primitive) if G doesn't contain any proper subgroup (resp. any proper normal subgroup) whose induced action on M is transitive as well. The aim of the present work is to investigate some combinatory properties of sym…

To any connected and simply connected nilpotent Lie group N, one can associate its group of affine transformations Aff(N). In this paper, we study simply transitive actions of a given nilpotent Lie group G on another nilpotent Lie group N, via such affine transformations. We succeed in translating the existence questio…

We extend the equivariant holomorphic Morse inequalities of circle actions to cases with torus and non-Abelian group actions on holomorphic vector bundles over Kahler manifolds and show the necessity of the Kahler condition. For torus actions, there is a set of inequalities for each choice of action chambers specifying…

Semisimple Lie groups act transitively on pseudo-Riemannian manifolds, making them flat.

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

PQR estimates reward functions from actions and states without assuming state-only rewards.

This paper shows how post-Lie algebra structures can be induced by simply transitive NIL-affine actions.

Classifies actions on complex space forms with Lagrangian orbits.

A locally conformally Kähler (LCK) manifold is a complex manifold whose universal cover is Kähler with monodromy group acting on the universal cover by holomorphic homotheties. A Vaisman manifold $M$ is a compact non-Kähler LCK manifold admitting an action of a holomorphic conformal flow lifting to an action on a Kähle…

On a generalized complex manifold there is an associated definition of a generalized holomorphic bundle, introduced by Gualtieri. This notion in the case of an ordinary complex structure yields an object which we call a co-Higgs bundle and we consider the B-field action of a closed form of type (1,1), both local and gl…

Constructs the moduli space of super J-holomorphic curves.

Study the geometry of twistor spaces with rotating circle action.

We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a…

A new RL paradigm reduces state-action-value function approximation inefficiency.

Formula derived for torsion of modified Dirac operator.

For simple and simply-connected complex algebraic group G, we conjecture the existence of a functor eta_G from the category of 2-bordisms to the category of holomorphic symplectic varieties with Hamiltonian action, such that gluing of boundaries corresponds to the holomorphic symplectic quotient with respect to the dia…

Develops Lie algebraic approach for compact complex homogeneous manifolds.

Let $M$ be an irreducible smooth complex projective variety equipped with an action of a compact Lie group $G$, and let $({\mathcal L},h)$ be a $G$-equivariant holomorphic Hermitian line bundle on $M$. Given a compact connected Riemann surface $X$, we construct a $G$-equivariant holomorphic Hermitian line bundle $(L\,,…

A visible action on a complex manifold is a holomorphic action that admits a $J$-transversal totally real submanifold $S$. It is said to be strongly visible if there exists an orbit-preserving anti-holomorphic diffeomorphism $σ$ such that $σ|_S = \mathrm{id}$. In this paper, we prove that for any Hermitian symmetric sp…

We define relative Gromov-Witten invariants and establish a general gluing theory of pseudo-holomorphic curves for symplectic cutting and contact surgery. Then, we use our general gluing theory to study the change of GW-invariants of Calabi-Yau 3-folds tranform under flops and extremal transitions. We prove a complete …

Holomorphic tensors on algebraic cones are invariant under certain group actions.

Study of pseudo-Riemannian manifolds with M{ö}bius group actions.

We classify the polar actions on the complex hyperbolic plane up to orbit equivalence. Apart from the trivial and transitive polar actions, there are five polar actions of cohomogeneity one and four polar actions of cohomogeneity two.

The paper develops a local index formula for complex manifolds with $\mathbb{C}^{\ast }$-action.

We study the holomorphic symplectic structures on hyper-Kaehler manifolds of type A_{\infty}, by using the torus action.

DPN combines model-based and model-free reinforcement learning for efficient planning.

Cusped hyperbolic 3-manifolds can have up to 4 cusps under certain group actions.

We give an affirmative answer to the Halperin-Carlsson conjecture for the homologically injective torus actions on closed manifolds. This class contains holomorphic torus actions on compact Kahler manifolds, torus actions on compact Riemannian flat manifolds.

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

Study of flows on 7D manifolds with holomorphic properties.

A homogeneous space is a manifold on which a Lie group acts transitively. Super generalization of this concept is also studied in [2] and [4]. In this paper we explicitly show that super Lie group GL(m|n) acts transitively on supergrassmannian G_{k|l}(m|n). In this regard, by using functor of point approach, this actio…