Related papers: A construction of SKT manifolds using toric geomet…

Let $P_m(J)$ denote a simplicial complex obtainable from consecutive wedge operations from an $m$-gon. In this paper, we completely classify toric manifolds over $P_m(J)$ and prove that all of them are projective. As a consequence, we…

We present the construction of a large class of homogeneous KT, HKT and QKT manifolds, $G/K$, using an invariant metric on $G$ and the canonical connection. For this a decomposition of the Lie algebra of $G$ is employed, which is most…

For a complex manifold $(M,J)$, an SKT (or pluriclosed) metric is a $J$-Hermitian metric $g$ whose fundamental form $\omega:=g(J\cdot,\cdot)$ satisfies the condition $\partial\overline{\partial}\omega=0$. As such, an SKT metric can be…

We give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the…

A strong KT (SKT) manifold consists of a Hermitian structure whose torsion three-form is closed. We classify the invariant SKT structures on four-dimensional solvable Lie groups. The classification includes solutions on groups that do not…

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…

I construct infinite families of knots and links with totally geodesic spanning surfaces, which we call TGS knots and TGS links, in various 3-manifolds. These 3-manifolds include thickened orientable surfaces, the sphere cross the circle,…

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…

We construct a new family of toric manifolds generating the unitary bordism ring. Each manifold in the family is the complex projectivisation of the sum of a line bundle and a trivial bundle over a complex projective space. We also…

Three-dimensional smooth, compact toric varieties (SCTV), when viewed as real six-dimensional manifolds, can admit G-structures rendering them suitable for internal manifolds in supersymmetric flux compactifications. We develop techniques…

We describe various constructions in Sasakian geometry. First we generalize the join construction of the first two authors to arbitrary Sasakian manifolds. We then give several examples, including ones which prove the existence of…

The simplicial wedge construction on simplicial complexes and simple polytopes has been used by a variety of authors to study toric and related spaces, including non-singular toric varieties, toric manifolds, intersections of quadrics and…

We use the geometry of the space of fields for gauged supersymmetric mechanics to construct the twisted differential equivariant K-theory of a manifold with an action by a finite group.

For an almost contact metric manifold $N$, we find conditions for which either the total space of an $S^1$-bundle over $N$ or the Riemannian cone over $N$ admits a strong K\"ahler with torsion (SKT) structure. In this way we construct new…

The K-rings of non-singular complex pro jective varieties as well as quasi- toric manifolds were described in terms of generators and relations in an earlier work of the author with V. Uma. In this paper we obtain a similar description for…

Let $X$ be the wonderful compactification of a complex adjoint symmetric space $G/K$ such that $rk(G/K)=rk(G)-rk(K)$. We show how to extend equivariant vector bundles on $G/K$ to equivariant vector bundles on $X$, generated by their global…

Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the…

We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields $\K$, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems.…

In the present paper we provide a construction via mapping tori of (non Bismut flat) strong HKT and generalized hyperk\"ahler structures on compact manifolds. The skew-symmetric torsion is parallel, but the manifolds are not a product of a…

We construct an infinite sequence of projectively flat manifolds by using castling transformations of prehomogeneous vector spaces. We also give a classification of manifolds equipped with a flat projective structure obtained by a finite…