9,514 research outputs found
Hermitian structures on six dimensional nilmanifolds
Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant
complex structure J and compatible metric g, which is not required to be
invariant. We give classifications of 6-dimensional nilmanifolds M admitting
strong K\"ahler with torsion, balanced or locally conformal K\"ahler structures
(J,g).Comment: LaTeX, 24 pages, 1 figur
Symplectic harmonicity and generalized coeffective cohomologies
Relations between the symplectically harmonic cohomology and the coeffective
cohomology of a symplectic manifold are obtained. This is achieved through a
generalization of the latter, which in addition allows us to provide a
coeffective version of the filtered cohomologies introduced by C.-J. Tsai,
L.-S. Tseng and S.-T. Yau. We construct closed (simply connected) manifolds
endowed with a family of symplectic forms such that the dimensions
of these symplectic cohomology groups vary with respect to . A complete
study of these cohomologies is given for 6-dimensional symplectic nilmanifolds,
and concrete examples with special cohomological properties are obtained on an
-dimensional solvmanifold and on 2-step nilmanifolds in higher dimensions.Comment: 25 pages; revised version, new Theorem 5.7 and Section 8 added,
references update
On the Strominger system and holomorphic deformations
We show that the property of existence of solution to the Strominger system
in dimension six is neither open nor closed under holomorphic deformations of
the complex structure. These results are obtained both in the case of positive
slope parameter as well as in the case of negative slope parameter in the
anomaly cancellation equation
Orientational melting of two-shell carbon nanoparticles: molecular dynamics study
The energetic characteristics of two-shell carbon nanoparticles ("onions")
with different shapes of second shell are calculated. The barriers of relative
rotation of shells are found to be surprisingly small; therefore, free relative
rotation of shells can take place at room temperature. The intershell
orientational melting of the nanoparticle is studied by
molecular dynamics. The parameters of Arrhenius formula for jump rotational
intershell diffusion are calculated. The definition of orientational melting
temperature is proposed as the temperature when the transition probability over
barrier between equivalent potential minima is equal to 1/2. The temperature of
orientational melting of the nanoparticle is about 60 K.Comment: 9 pages, 10 figures, some new simulation results and formulations
introduce
Six dimensional solvmanifolds with holomorphically trivial canonical bundle
We determine the 6-dimensional solvmanifolds admitting an invariant complex
structure with holomorphically trivial canonical bundle. Such complex
structures are classified up to isomorphism, and the existence of strong
K\"ahler with torsion (SKT), generalized Gauduchon, balanced and strongly
Gauduchon metrics is studied. As an application we construct a holomorphic
family of compact complex manifolds such that satisfies the
-Lemma and admits a balanced metric for any ,
but the central limit neither satisfies the -Lemma nor
admits balanced metrics.Comment: 32 pages; to appear in IMR
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