Related papers: A-manifolds on a principal torus bundle over an A-…
We characterize the geometric moduli of non-Kaehler manifolds with torsion. Heterotic supersymmetric flux compactifications require that the six-dimensional internal manifold be balanced, the gauge bundle be hermitian Yang-Mills, and also…
New heterotic torsional geometries are constructed as orbifolds of T^2 bundles over K3. The discrete symmetries considered can be freely-acting or have fixed points and/or fixed curves. We give explicit constructions when the base K3 is…
We discuss F-theory backgrounds associated to flat torus bundles over Ricci-flat manifolds. In this setting the F-theory background can be understood as a IIB orientifold with a large radius limit described by a supersymmetric…
We consider a particular class of holomorphic vector bundles relevant for supersymmetric string theory, called \emph{omalous}, over nonsingular projective varieties. We use monads to construct examples of such bundles over 3-fold…
Given a Lie group G, one constructs a principal G-bundle on a manifold X by taking a cover U of X, specifying a transition cocycle on the cover, and descending the trivialized bundle along the cover. We demonstrate the existence of an…
This paper gives an example of special Lagrangian manifold obtained from a hypersurface of a complex Grassmannian with vanishing first Chern class. The obtained manifold is a 1-torus bundle over the two dimensional real projective space.…
We study the properties of Ricci curvature of ${\mathfrak{g}}$-manifolds with particular attention paid to higher dimensional abelian Lie algebra case. The relations between Ricci curvature of the manifold and the Ricci curvature of the…
We describe a necessary and sufficient condition for a principal circle bundle over an even-dimensional manifold to carry an invariant contact structure. As a corollary it is shown that all circle bundles over a given base manifold carry an…
We classify incompressible, boundary-incompressible, nonorientable surfaces in punctured-torus bundles over $S^1$. We use the ideas of Floyd, Hatcher, and Thurston. The main tool is to put our surface in the "Morse position" with respect to…
We show the existence of special Lagrangian tori on one family of Borcea-Voisin threefolds. We also construct a family of special Lagrangian submanifolds on the total space of the canonical line bundle of projective spaces.
I point out some very elementary examples of special Lagrangian tori in certain Calabi-Yau manifolds that occur as hypersurfaces in complex projective space. All of these are constructed as real slices of smooth hypersurfaces defined over…
Spectral triples over noncommutative principal $\T^n$-bundles are studied, extending recent results about the noncommutative geometry of principal U(1)-bundles. We relate the noncommutative geometry of the total space of the bundle with the…
A series of examples of toric Sasaki-Einstein 5-manifolds is constructed. These are submanifolds of toric 3-Sasaki 7-manifolds and such a Sasaki-Einstein 5-manifold corresponds uniquely to a toric 3-Sasaki 7-manifold. This produces examples…
Given a hypercomplex manifold with a rotating vector field (and additional data), we construct a conical hypercomplex manifold. As a consequence, we associate a quaternionic manifold to a hypercomplex manifold of the same dimension with a…
Toric hyperk{\"a}hler manifolds are quaternion analog of toric varieties. Bielawski pointed out that they can be glued by cotangent bundles of toric varieties. Following his idea, viewing both toric varieties and toric hyperk{\"a}her…
In this paper we study the class of compact K\"ahler manifolds with positive orthogonal Ricci curvature: $Ric^\perp>0$. First we illustrate examples of K\"ahler manifolds with $Ric^\perp>0$ on K\"ahler C-spaces, and construct ones on…
A large number of examples of compact $G_2$ manifolds, relevant to supersymmetric compactifications of M-Theory to four dimensions, can be constructed by forming a twisted connected sum of two appropriate building blocks times a circle.…
Using a recently developed piecewise flat method, numerical evolutions of the Ricci flow are computed for a number of manifolds, using a number of different mesh types, and shown to converge to the expected smooth behaviour as the mesh…
We construct globally-defined $SU(3)$ structures on smooth compact toric varieties (SCTV) in the class of $\mathbb{CP}^1$ bundles over $M$, where $M$ is an arbitrary SCTV of complex dimension two. The construction can be extended to the…
Riemannian metrics of positive Ricci curvature were constructed on certain moment-angle manifolds.