1,246 research outputs found
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 real homotopy type of generalized complex nilmanifolds
We prove that for any there are infinitely many real homotopy types
of -dimensional nilmanifolds admitting generalized complex structures of
every type , for . This is in deep contrast to the
-dimensional case.Comment: 11 pages; observation added concerning higher dimensions; change of
title and abstrac
Invariant solutions to the Strominger system and the heterotic equations of motion
We construct many new invariant solutions to the Strominger system with
respect to a 2-parameter family of metric connections
in the anomaly cancellation equation. The ansatz
is a natural extension of the canonical 1-parameter
family of Hermitian connections found by Gauduchon, as one recovers the Chern
connection for , and the Bismut
connection for . In particular,
explicit invariant solutions to the Strominger system with respect to the Chern
connection, with non-flat instanton and positive are obtained.
Furthermore, we give invariant solutions to the heterotic equations of motion
with respect to the Bismut connection. Our solutions live on three different
compact non-K\"ahler homogeneous spaces, obtained as the quotient by a lattice
of maximal rank of a nilpotent Lie group, the semisimple group
SL(2,) and a solvable Lie group. To our knowledge, these are the
only known invariant solutions to the heterotic equations of motion, and we
conjecture that there is no other such homogeneous space admitting an invariant
solution to the heterotic equations of motion with respect to a connection in
the ansatz .Comment: 27 pages, 3 figure
A family of complex nilmanifolds with infinitely many real homotopy types
We find a one-parameter family of non-isomorphic nilpotent Lie algebras
, with , of real dimension eight with
(strongly non-nilpotent) complex structures. By restricting to take
rational values, we arrive at the existence of infinitely many real homotopy
types of -dimensional nilmanifolds admitting a complex structure. Moreover,
balanced Hermitian metrics and generalized Gauduchon metrics on such
nilmanifolds are constructed.Comment: 15 page
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