Raquel Villacampa

Non-Kaehler Heterotic String Compactifications with Non-Zero Fluxes and Constant Dilaton

We construct new explicit compact supersymmetric valid solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic equations of motion in dimension six. We present balanced Hermitian structures on compact nilmanifolds in dimension six satisfying the heterotic supersymmetry equations with non-zero flux, non-flat instanton and constant dilaton which obey the three-form Bianchi identity with curvature term taken with respect to either the Levi-Civita, the (+)-connection or the Chern connection. Among them, all our solutions with respect to the (+)-connection on the compact nilmanifold M3 satisfy the heterotic equations of motion.

On the Bott-Chern cohomology and balanced Hermitian nilmanifolds

The Bott–Chern cohomology of six-dimensional nilmanifolds endowed with invariant complex structure is studied with special attention to the cases when balanced or strongly Gauduchon Hermitian metrics exist. We consider complex invariants introduced by Angella and Tomassini and by Schweitzer, which are related to the -lemma condition and defined in terms of the Bott–Chern cohomology, and show that the vanishing of some of these invariants is not a closed property under holomorphic deformations. In the balanced case, we determine the spaces that parametrize deformations in type IIB supergravity described by Tseng and Yau in terms of the Bott–Chern cohomology group of bidegree (2, 2).

Compact supersymmetric solutions of the heterotic equations of motion in dimensions 7 and 8

Abstract We construct explicit compact supersymmetric solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic string equations in dimension five. We present a quadratic condition on the curvature which is necessary and sufficient the heterotic supersymmetry and the anomaly cancellation to imply the heterotic equations of motion in dimension five. We supply compact nilmanifold in dimension 5 satisfying the heterotic supersymmetry equations with non-zero fluxes and constant dilaton which obeys the three-form Bianchi identity and solves the heterotic equations of motion in dimension five.

Balanced Hermitian metrics from SU(2)-structures

We study the intrinsic geometrical structure of hypersurfaces in six-manifolds carrying a balanced Hermitian SU(3)-structure, which we call balanced SU(2)-structure. We provide sufficient conditions, in terms of suitable evolution equations, which imply that a five-manifold with such structure can be isometrically embedded as a hypersurface in a balanced Hermitian SU(3)-manifold. Any five-dimensional compact nilmanifold has an invariant balanced SU(2)-structure, and we show how some of them can be evolved to give new explicit examples of balanced Hermitian SU(3)-structures. Moreover, for n=3,4, we present examples of compact solvmanifolds endowed with a balanced SU(n)-structure such that the corresponding Bismut connection has holonomy equal to SU(n).

HKT structures from almost contact manifolds

We review some results on hyper‐Kahler with torsion (HKT) structures on the total space of an S1‐bundle over manifolds with three almost contact structures. Moreover, we show that deforming slightly the metric on the S1‐bundle one may obtain an HKT structure starting from a 3‐Sasakian structure, which allows us to construct examples of HKT structures from a 3‐Sasakian structure on a certain Aloff‐Wallach space.

ON COHOMOLOGICAL DECOMPOSITION OF BALANCED MANIFOLDS

We study complex-pure-and-fullness at the first stage on compact complex nilmanifolds M of complex dimension 3, with special attention to the case of existence of a balanced Hermitian metric on M.

A Family of Complex Nilmanifolds with in finitely Many Real Homotopy Types

Abstract We find a one-parameter family of non-isomorphic nilpotent Lie algebras ga, with a > [0,∞), of real dimension eight with (strongly non-nilpotent) complex structures. By restricting a to take rational values, we arrive at the existence of infinitely many real homotopy types of 8-dimensional nilmanifolds admitting a complex structure. Moreover, balanced Hermitian metrics and generalized Gauduchon metrics on such nilmanifolds are constructed.

Hermitian Metrics on Compact Complex Manifolds and Their Deformation Limits

We consider various types of special Hermitian metrics on compact complex manifolds, namely Kahler, Hermitian-symplectic, SKT, balanced and strongly Gauduchon metrics. We study the strongly Gauduchon metrics in relation to the SKT condition on complex nilmanifolds and to the Hermitian-symplectic condition on certain complex solvmanifolds. We also review the behaviour of the existence properties of these special metrics on compact complex manifolds under holomorphic deformations.

Balanced and strongly Gauduchon cones on solvmanifolds

We show conditions under which the balanced and strongly Gauduchon cones of a complex solvmanifold are non-degenerate. These cones are explicitly described on the complex nilmanifolds with underlying Lie algebra

On Special Hermitian Geometry

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