Results 51 to 60 of about 1,038 (85)

Holomorphic Cartan geometries and rational curves

Complex Manifolds, 2016
We prove that any compact Kähler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact Kähler manifold.
Biswas Indranil, McKay Benjamin
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A Note on the L2-norm of the Second Fundamental Form of Algebraic Manifolds [PDF]

, 2010
2000 Mathematics Subject Classification: 53C42, 53C55.Let M f → CP^n be an algebraic manifold of complex dimension d and let σf be its second fundamental form. In this paper we address the following conjecture, which is the analogue of the one stated by
Loi, Andrea, Zedda, Michela
core  

Toric extremal Kähler-Ricci solitons are Kähler-Einstein

Complex Manifolds, 2017
In this short note, we prove that a Calabi extremal Kähler-Ricci soliton on a compact toric Kähler manifold is Einstein. This settles for the class of toric manifolds a general problem stated by the authors that they solved only under some curvature ...
Calamai Simone, Petrecca David
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Locally conformally K\"ahler manifolds with holomorphic Lee field

, 2017
We prove that a compact lcK manifold with holomorphic Lee vector field is Vaisman provided that either the Lee field has constant norm or the metric is Gauduchon (i.e., the Lee field is divergence-free).
Moroianu, Andrei, Moroianu, Sergiu, Ornea, Liviu   +2 more
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Examples of solvmanifolds without LCK structures

Complex Manifolds, 2018
The purpose in this paper is to construct solvmanifolds without LCK structures such that the complex structure is left ...
Sawai Hiroshi
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Tamed symplectic structures on compact solvmanifolds of completely solvable type [PDF]

, 2015
A compact solvmanifold of completely solvable type, i.e. a compact quotient of a completely solvable Lie group by a lattice, has a K\"ahler structure if and only if it is a complex torus.
Fino, Anna, Kasuya, Hisashi
core  

On Kähler-like and G-Kähler-like almost Hermitian manifolds

Complex Manifolds, 2020
We introduce Kähler-like, G-Kähler-like metrics on almost Hermitian manifolds. We prove that a compact Kähler-like and G-Kähler-like almost Hermitian manifold equipped with an almost balanced metric is Kähler.
Kawamura Masaya
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Geodesics and magnetic curves in the 4-dim almost Kähler model space F4

Complex Manifolds
We study geodesics and magnetic trajectories in the model space F4{{\rm{F}}}^{4}. The space F4{{\rm{F}}}^{4} is isometric to the 4-dim simply connected Riemannian 3-symmetric space due to Kowalski. We describe the solvable Lie group model of F4{{\rm{F}}}^
Erjavec Zlatko, Inoguchi Jun-ichi
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H-functional and Matsushima type decomposition theorem

, 2019
The H-functional characterizes K\"ahler-Ricci solitons as its critical points, and also plays an important role of the existence problem for K\"ahler-Einstein metrics. In this paper we prove the Hessian formula for the H-functional at its critical points,
Nakamura, Satoshi
core  

On the Kähler-likeness on almost Hermitian manifolds

Complex Manifolds, 2019
We define a Kähler-like almost Hermitian metric. We will prove that on a compact Kähler-like almost Hermitian manifold (M2n, J, g), if it admits a positive ∂ ̄∂-closed (n − 2, n − 2)-form, then g is a quasi-Kähler metric.
Kawamura Masaya
doaj   +1 more source