Results 41 to 50 of about 97 (90)

Orientations and Geometrisations of Compact Complex Surfaces [PDF]

, 2017
Every complex manifold carries a canonical orientation, and it is natural to wonder when the underlying topological or smooth manifold carries a complex structure compatible with the other orientation.
Kotschick, D.
core  

RC-positive metrics on rationally connected manifolds

Forum of Mathematics, Sigma, 2020
In this paper, we prove that if a compact Kähler manifold X has a smooth Hermitian metric $\omega $ such that $(T_X,\omega )$ is uniformly RC-positive, then X is projective and rationally connected. Conversely, we show that, if a projective
Xiaokui Yang
doaj   +1 more source

Second Chern-Einstein metrics on four-dimensional almost-Hermitian manifolds

Complex Manifolds, 2023
We study four-dimensional second Chern-Einstein almost-Hermitian manifolds. In the compact case, we observe that under a certain hypothesis, the Riemannian dual of the Lee form is a Killing vector field.
Barbaro Giuseppe, Lejmi Mehdi
doaj   +1 more source

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
doaj   +1 more source

On totally umbilical CR‐submanifolds of a Kaehler manifold

, 1992
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 405-408, 1993.
M. A. Bashir
wiley   +1 more source

Real hypersurfaces of indefinite Kaehler manifolds

, 1992
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 3, Page 545-556, 1993.
A. Bejancu, K. L. Duggal
wiley   +1 more source

On the rigidity of ℂℙ2n × ℂℙ1

Complex Manifolds
We revisit Koiso’s original examples of rigid infinitesimally deformable Einstein metrics. We show how to compute Koiso’s obstruction to the integrability of the infinitesimal deformations on CP2n×CP1{{\mathbb{CP}}}^{2n}\times {{\mathbb{CP}}}^{1} using ...
Hall Stuart James
doaj   +1 more source

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
doaj   +1 more source

Generalized Goldberg-Sachs Theorems for Pseudo-Riemannian Four-Manifolds

, 1996
[Apostolov Vestislav; Апостолов Вестислав]It has been recently observed that the Generalized Goldberg-Sachs Theorem in General Relativity as well as some of its corollaries admit appropriate Riemannian versions.
Apostolov, Vestislav
core   +1 more source

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
doaj   +1 more source