Related papers: Spinc structures on real Bott manifolds
In this paper we determine conditions of existence of an induced Riemannian structure on the symplectic quotient of a symplectic and Riemannian manifold following the action of a Lie group acting upon it in a hamiltonian way with…
The aim of this paper is the construction of spinor bundles of Cartan type over certain non-orientable manifolds.
Any bounding compact smooth manifold bounds a compact manifold with a spine consisting of transversely intersecting codimension one submanifolds. This paper provides details for a picture proof given in previous papers with S. Akbulut.
We give a necessary and sufficient condition for a generalized Bott manifold to be Fano or weak Fano. As a consequence we characterize Fano Bott manifolds.
An important open question in G$_{2}$ geometry concerns whether or not a compact seven-manifold can support an exact G$_{2}$-Structure. Given the significance of this question we initiate a study of exact G$_{2}$-Structures on compact…
Spherically symmetric thin-shell wormholes are constructed within the framework of Brans-Dicke gravity. It is shown that, for appropriate values of the Brans-Dicke constant, these wormholes can be supported by matter satisfying the energy…
In this paper, we show the existence of (co-oriented) contact structures on certain classes of $G_2$-manifolds, and that these two structures are compatible in certain ways. Moreover, we prove that any seven-manifold with a spin structure…
We prove necessary and sufficient conditions for a smooth surface in a 4-manifold X to be pseudoholomorphic with respect to some almost complex structure on X. This provides a systematic approach to the construction of pseudoholomorphic…
We give a set of sufficient and necessary conditions for parabolicity and hyperbolicity of a submanifold with controlled mean curvature in a Riemannian manifold with a pole and with sectional curvatures bounded from above or from below.
We study the rigidity of compact submanifolds of Riemannian manifolds of arbitrary codimension that satisfy a sharp pinching condition involving the norm of the second fundamental form and the mean curvature. Without assuming that the…
We prove the existence of flips in dimension n, contingent on the termination of real flips in dimension n-1.
We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…
We establish the existence of models of quadric surface bundles with prescribed \'etale local forms.
We show the strong cohomological rigidity of Hirzebruch surface bundles over Bott manifolds. As a corollary, we have that the strong cohomological rigidity conjecture is true for Bott manifolds of dimension $8$.
Classically, a spin structure on the loop space of a manifold is a lift of the structure group of the looped frame bundle from the loop group to its universal central extension. Heuristically, the loop space of a manifold is spin if and…
We show that a topological symplectic manifold has a canonically associated bi-Lipschitz structure. As a corollary, we obtain the first examples of non-existence and non-uniqueness for topological symplectic structures. Our arguments hold…
We study the integrability of a (almost) complex structure calibrated by a symplectic form. We find new sufficent conditions.
The theme is the influence of the spin structure on the Dirac spectrum of a spin manifold. We survey examples and results related to this question.
In this paper we construct a family of simply connected, spin, non-complex, symplectic 4-manifolds which cover all but finitely many allowed lattice points $(\chi, c)$ lying in $0 \leq c \leq 8.76\chi$. Furthermore, as a corollary, we prove…
We give a necessary and sufficient condition for a set of left invariant metrics on a compact Heisenberg manifold to be relatively compact in the corresponding moduli space.