In this paper, first we give a notion for linear Weingarten spacelike hypersurfaces with P + aH = b in a locally symmetric Lorentz space Ln+1 1 . Furthermore, we study complete or compact linear Weingarten spacelike hypersurfaces in locally symmetric Lorentz spaces Ln+1 1 satisfying some curvature conditions. By modifying Cheng-Yau’s operator given in [7], we introduce a modified operator L and...

We provide a systematic treatment of possible corrections to the inflaton potential for D-brane inflation in the warped deformed conifold. We consider the D3-brane potential in the presence of the most general possible corrections to the throat geometry sourced by coupling to the bulk of a compact Calabi-Yau space. This corresponds to the potential on the Coulomb branch of the dual gauge theory...

We explore differential and algebraic operations on the exterior product of spinor representations and their twists that give rise to cohomology, the spin cohomology. A linear differential operator d is introduced which is associated to a connection ∇ and a parallel spinor ζ, ∇ζ = 0, and the algebraic operators D(p) are constructed from skew-products of p gamma matrices. We exhibit a large numb...

In this paper, we consider the characterization of eigenfunctions for Laplacian operators on some Riemannian manifolds. Firstly we prove that for the space form (M K , gK) with the constant sectional curvature K, the first eigenvalue of Laplacian operator λ1 (M K) is greater than the limit of the first Dirichlet eigenvalue of Laplacian operator λ1 (BK (p, r)). Based on this, we then present a c...

The almost splitting theorem of Cheeger-Colding is established in the setting nonnegative generalized m-Bakry–Émery Ricci curvature, which m positive and associated vector field not necessarily required to be gradient a function. In this context it shown that with diameter upper bound volume lower bound, as well control on Bakry–Émery field, fundamental group such manifolds abelian. Furthermore...

Moreover we know exactly when the equality holds: if and only if D is a disc. For any optimal geometric inequality it is important to have a complete understanding of the equality case. Sometimes this can be easily achieved by checking the proof of the inequality. Take as an example the following elegant theorem due to Lichenerowicz [L]: let (M; g) be a compact Riemannian manifold of dimension ...

Ken Cheng was born in Hong Kong. His family emigrated to Toronto, Canada while he was still young, and he attended high school in Toronto, and then the University of Toronto. He has a M.Ed. from Harvard University and a Ph.D. from the University of Pennsylvania in Philadelphia, USA in 1984. He did postdoctoral work at the University of Sussex and at the University of Western Ontario before beco...

This is the sequel to my preprint“TCFTs and Calabi-Yau categories”. Here we extend the results of that paper to construct, for certain Calabi-Yau A∞ categories, something playing the role of the Gromov-Witten potential. This is a state in the Fock space associated to periodic cyclic homology, which is a symplectic vector space. Applying this to a suitable A∞ version of the derived category of s...

The singular cochain complex of a topological space is a classical object. It is a Differential Graded algebra which has been studied intensively with a range of methods, not least within rational homotopy theory. More recently, the tools of Auslander-Reiten theory have also been applied to the singular cochain complex. One of the highlights is that by these methods, each Poincaré duality space...