# Tagged Questions

2answers
259 views

### Is the Nijenhuis tensor an obstruction to the existence of non constant pseudo-holomorphic maps?

Let $(N,J_N)$ and $(M, J_M)$ be two compact almost complex manifolds with non integrable almost complex structures (i.e., the Nijenhuis tensor is non zero for both $J_N$ and $J_M$). Does it imply ...
1answer
421 views

### Geometric interpretation for fourth coeficient of the polynomial for Hirzebruch–Riemann–Roch theorem

Hey guys :) I have a question on a theorem which is known as Tian-Yau-Zelditch theorem now. If there is some reference for following question, please let me know Let $(M,\omega)$ be a compact ...
1answer
291 views

1answer
366 views

### A question about Marsden-Weinstein reduction theory

Let $G$ ba a compat Lie group and $\frak g$ be its Lie algebra, then by Marsden-Weinstein reduction theory we know that if we take $M=T^*G$ and $J:M\to \frak g^*$ be its moment map then the reduced ...
0answers
105 views

### Moment map in the singular case

The moment map is defined on the symplectic manifold $(M,\omega)$, or particularly, $(M,\omega)$ is Kahler. While $\omega$ is smooth or differential enough, the definition is obvious to understand, in ...
1answer
215 views

### Cotangent bundle of coadjoint orbit is stein manifold?

Let me first define stein manifolds and coadjoint orbits. A complex manifold $X$ of complex dimension $n$ is called a Stein manifold if the following conditions hold: $X$ is holomorphically convex, ...
0answers
83 views

### filling by holomorphic disks method

Can you give me a reference for the proof of the filling by holomorphic disks method, besides Bishop's original paper?
1answer
263 views

2answers
286 views

### Uniqueness of Kähler form with same volume

Hallo, Let $M$ be a compact real-analytic Riemannian manifold with Riemannian metric $g$. Let $U \subset T^{*}M$ be a open neighbourhood of the zero section. On $U$ there exists a complex structure ...
1answer
598 views

### an extended question of Gromov: Every **generalized open almost complex manifold** admits a **generalized symplectic structure**? [closed]

Definition (Open Manifolds):An open manifold is a manifold without boundary with no compact component. For a connected manifold, "open" is equivalent to "without boundary and non-compact. we know that ...
1answer
188 views

### Hamiltonian polar action with Lagrangian section

I am looking for examples of Hamiltonian polar isometric actions of a compact Lie group on a Kahler-Einstein (or perhaps just Kahler) manifold, that admits a Lagrangian section. Recall that an ...
1answer
135 views

### Isometric embedding of a neighbourhood of a totally real submanifold in a Kähler manifold

Hallo, Let $(M,J,\omega)$ be a real-analytic Kähler manifold. Let furthermore $A \subset M$ be a real analytic, totally real, Lagrangian submanifold and set $g := h|_{A}$. Where $h$ is the Kähler ...
0answers
168 views

### Different complexifications of a real analytic Riemannian manifold

Hi, I have a question concerning the complexification of a real analytic Riemannian manifold. Let $(M,g)$ be a compact Riemannian manifold. It is a well knwon fact that in a neighbourhood $U$ of the ...
1answer
188 views

### Isometric embedding of a real-analytic Riemannian manifold in a compact Kähler manifold

Hallo, It is a known fact that any real-analytic Riemannian manifold $M$ admits a isometric embedding in a Kähler manifold $\Omega$, where $M$ is totally real in $\Omega$. Of $\Omega$ can be taught ...
2answers
270 views

### Analytic Lagrangian Submanifolds

Hallo, I am looking for a preprint "Analytic Lagrangian Submanifolds" by Guillemin, Sternberg. I googled it but without any success. Does any one know how I could get this preprint. Or are there ...
1answer
222 views

### Polarisation in a nighbourhood of a Lagrangian submanifold

Hallo, Let $(X, \omega)$ be a symplectic manifold of dimension $2n$ and $\omega$ is an exact symplectic form i.e. $\omega = -d\alpha$. Let furthermore $M \subset X$ be a Lagrangian submanifold such ...
0answers
116 views

### Relation between Adpted Complex Structure and Hyperkaehler Structure

Hallo, I am reading the paper "Hyperkaehler structures on total spaces of holomorphic cotangent bundles" by Kaledin where he puts a hyperkähler structure on a neigbourhood of the $0$-section in the ...
1answer
265 views

### Holonomy group of a non-compact Kaehler manifold

Hallo, I have the following question: Let $(M,I,\omega)$ be a not necessary compact Kaehler manifold of complex dimension $n$. Assume that there exists a nowhere vanishing holomorphic $(n,0)$-form ...
1answer
374 views

### complete or open Kähler manifold and simply connected

A complete or open Káhler manifold with positive definite Ricci tensor is simply connected? is there any counterexample?
0answers
351 views

### A generalization of Liouville formula for the determinant of a system of ODE?

Let $\Phi(t)$ be an $n\times n$ complex matrix whose columns are (independent) solutions of the system of ordinary differential equations (ODE): $\frac{d}{dt}y= A(t) y$, where $A(t)$ is a ...
1answer
411 views

### Holonomy group of calabi yau manifold

Let $(M,J,\omega, \Omega)$ be a calabi-yau manifold (not necessary compact). Does it follow that the holonomy group of $M$ is $SU_{n}$, where $n$ is the complex dimension of $M$ ?
1answer
373 views

### Fishy version of Kodaira embedding theorem !

Is there any theorem characterizing those sypmlectic manifolds that can be embedded symplectically in projective space equipped with Fubini-Study symplectic form?
3answers
550 views

### Kähler structure on a complex reductive group

Let $G$ be a complex reductive group, and $K$ a maximal compact subgroup (such that $K_{\mathbb{C}}=G$). By the polar decomposition theorem one has that, as manifolds, $G\cong T^*K$. The inherited ...
0answers
374 views

### About automorphisms of ratonal surfaces.

Hi. I have a question about automorphisms of smooth ratonal surfaces. (I am not an algebraic geometer, so my question could be stupid. I am sorry about that.) Let $X_k$ be a blow-up of $\mathbb{P}^2$ ...
3answers
440 views

### symplectic form with partition on unity

Assume $M$ is a $2n-$dimensional differentiable manifold. Let $(U_{i})$ be a open covering of $M$. With respect to this covering let $\rho_{i}$ be a partition of unity. Assume that on each $U_{i}$ we ...
1answer
405 views

### “monotone” versus “symplectic Fano”

Hi. I have a question about the notion "symplectic Fano". Let $(M,\omega)$ be a symplectic manifold with a $\omega$-tamed almost complex structure $J$. According to "J-holomorphic curves and ...
1answer
309 views