In a previous paper [ M. Hanada, H. Kawai and Y. Kimura, Prog. Theor. Phys. 114 (2005), 1295 ] it is shown that a covariant derivative on any n-dimensional Riemannian manifold can be expressed in terms of a set of n matrices, and a new interpretation of IIB matrix model, in which the diffeomorphism, the local Lorentz symmetry and their higher spin analogues are embedded in the unitary symmetry,...

Let (M,g) be an oriented Lorentzian 4-manifold, and consider the space S of oriented, unparameterized time-like 2-surfaces in M (string world-sheets) with fixed boundary conditions. Then the infinitedimensional manifold S carries a natural complex structure and a compatible (positive-definite) Kähler metric h on S determined by the Lorentz metric g. Similar results are proved for other dimensio...

We prove that every Kähler metric, whose potential is a function of the timelike distance in the flat Kähler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local classification of the Kähler manifolds with the above mentioned metrics. New examples of Sasakian space forms are obtained as real hypersurfaces of a Kähler space form ...

It is difficult to formulate general relativity on noncommutative spaces, and there are thus different approaches in the literature. In [1] for example a deformation of Einstein’s gravity was studied using a construction based on gauging the noncommutative SO(4,1) de Sitter group and the Seiberg-Witten map with subsequent contraction to ISO(3,1). Most recently constructions of a noncommutative ...

in this paper, we consider a class of connected oriented (with respect to z/p) closed g-manifolds with a non-empty finite fixed point set, each of which is g-equivariantly formal, where g = z/p and p is an odd prime. using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a g-manifold in terms of algebra. this makes it p...

In order to study the variation of electronic properties, a set of bithiophene derivatives has been ‎developed. Here, the effect of substitution on the aromaticity properties of some cyclic ‎bithiophene derivative compounds was investigated using theoretical calculations. Calculations ‎were performed at B3LYP/6-31+G (d,p) level; and calculated properties included energy, dipole ‎moment, total c...

in this paper, we obtain a necessary and sufficient condition for a conformal mapping between two weyl manifolds to preserve einstein tensor. then we prove that some basic curvature tensors of $w_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. also, we obtained the relation between the scalar curvatures of the weyl manifolds r...

Nonlinear analysis has played a prominent role in the recent developments in geometry and topology. The study of the Yang-Mills equation and its cousins gave rise to the Donaldson invariants and more recently, the Seiberg-Witten invariants. Those invariants have enabled us to prove a number of striking results for low dimensional manifolds, particularly, 4-manifolds. The theory of Gromov-Witten...

It is proved that every compact Lorentz manifold admitting a timelike conformai Killing vector field is geodesically complete. So, a recent result by Kamishima in J. Differential Geometry [37 (1993), 569-601] is widely extended. Recently, it has been proved in [2] that a compact Lorentz manifold of constant curvature admitting a timelike Killing vector field is (geodesically) complete. It is na...

We consider the region of closed timelike curves (CTC’s) in three-dimensional flat Lorentz spacetimes. The interest in this global geometrical feature goes beyond the purely mathematical. Such spacetimes may be considered lower-dimensional toy models of sourceless Einstein gravity or cosmology. In three dimensions all such spacetimes are known: they are quotients of Minkowski space by a suitabl...