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Torsion and cotorsion in the sheaf of Kähler differentials on some mild singularities
Torsion cotorsion sheaf of Kä hler differentials some mild singularities
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2011/3/1
We give a criterion for the sheaf of Kähler differentials on a cone over a smooth projective variety to be torsionfree.
The Tanno-Theorem for Kählerian metrics with arbitrary signature
Tanno-Theorem Kä hlerian metrics arbitrary signature
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2011/1/18
Considering a non-constant smooth solution f of the Tanno equation on a closed,connected K¨ahler manifold (M, g, J) with positively definite metric g, Tanno showed that the manifold can be finitely co...
Infinite bubbling in non-Kählerian geometry
Infinite non-Kä hlerian geometry
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2011/2/25
In a holomorphic family (Xb)b∈B of non-K¨ahlerian compact manifolds,the holomorphic curves representing a fixed 2-homology class do not form a proper family in general.
Kähler groups, real hyperbolic spaces and the Cremona group
Kä hler groups real hyperbolic spaces Cremona group
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2011/1/19
Generalizing a classical theorem of Carlson and Toledo, we prove that any Zariski dense isometric action of a K¨ahler group on the real hyperbolic space of dimension at least 3 factors through a homom...
Geometric Realizability of Covariant Derivative Kähler Tensors for almost Pseudo-Hermitian and almost Para-Hermitian Manifolds
Geometric Realizability Covariant Derivative Kä hler Tensors Pseudo-Hermitian
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2011/2/25
The covariant derivative of the K¨ahler form of an almost pseudo-Hermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which s...
Cusps of the Kähler moduli space and stability conditions on K3 surfaces
Cusps of the Kä hler moduli space stability conditions
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2011/1/21
In [Ma09] S. Ma established a bijection between Fourier–Mukai partners of a K3 surface and cusps of the K¨ahler moduli space.The K¨ahler moduli space can be described as a quotient of Bridgeland’s sta...
Noncommutative Positivstellensätze for pairs representation-vector
Noncommutative Positivstellensä tze pairs representation-vector
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2010/11/24
We study non-commutative real algebraic geometry for a unital associative *-algebra A viewing the points as pairs ({\pi},v) where {\pi} is an unbounded *-representation of A on an inner product space...
Kähler Ricci flow with vanished Futaki invariant
Kä hler Ricci Futaki invariant
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2010/11/24
We study the convergence of the K\"ahler-Ricci flow on a compact K\"ahler manifold $(M,J)$ with positive first Chern class $c_1(M;J)$ and vanished Futaki invariant on $\pi c_1(M;J)$. As the applicati...
Scalar--flat Kähler metrics with conformal Bianchi V symmetry
General Relativity and Quantum Cosmology (gr-qc) High Energy Physics - Theory (hep-th) Differential Geometry (math.DG) Exactly Solvable and Integrable Systems (nlin.SI)
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2010/11/11
We provide an affirmative answer to a question posed by Tod \cite{Tod:1995b}, and construct all four-dimensional Kahler metrics with vanishing scalar curvature which are invariant under the conformal ...
HyperKähler Potentials in Cohomogeneity Two
HyperKä hler Potentials Cohomogeneity Two
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2010/10/29
A hyperK\"ahler potential is a function rho that is a K\"ahler potential for each complex structure compatible with the hyperK\"ahler structure. Nilpotent orbits in a complex simple Lie algebra are kn...
Dynamics of automorphisms on compact Kähler manifolds
holomorphic automorphism Green current laminar current Green measure
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2010/12/14
We study holomorphic automorphisms on compact K¨ahler manifolds having simple actions on the Hodge cohomology ring. We show for such automorphisms that the main dynamical Green currents admit complex ...
Almost Kähler manifolds of constant antiholomorphic sectional curvature
Kä hler manifolds constant antiholomorphic sectional curvature
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2010/12/6
We prove that an AK2-manifold of dimension 2m ≥ 6 and of pointwise constant antiholomorphic
sectional curvature is either a 6-dimensional manifold of constant negative sectional curvature or is local...
Schur's theorem of antiholomorphic type for quasi-Kählerian manifolds
Schur's theorem antiholomorphic type quasi-Kä hlerian manifolds
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2010/12/6
Let M be an almost Hermitian manifold with dimM = 2n, a metric tensor g and an almost complex structure J. The Ricci tensor and the scalar curvature with regard to the curvature tensor R are denoted b...
Nearly Kähler manifolds of constant antiholomorphic sectional curvature
Kä hler manifolds constant antiholomorphic sectional curvature
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2010/12/6
In this paper we consider nearly K¨ahler manifolds of pointwise constant antiholomorphic
sectional curvature. An analogue of Schur’s theorem is proved and a classification theorem
for such manifolds...
Every closed Kähler manifold with degree of mobility $\ge 3$ is $(CP(n), g_{Fubini-Study})$
Every closed Kä hler manifold degree
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2010/12/14
The degree of mobility of a (pseudo-Riemannian) K¨ahler metric is the dimension of the space of metrics h-projectively equivalent to it. We prove that a metric on a closed connected manifold can not h...