This can be compared to the fact that a conformally flat manifold of dimension n > 2 is locally conformal to a region of the sphere of the same dimension. In twistor theory, it is well-known that an even dimensional conformally flat manifold has an integrable twistor space ([7], [6], [1], [3]). It is interesting, as an analogy, that a Bochner-Kähler manifold has integrable twistor spaces define...

We introduce the concept of quasi-semi-Weyl structure, we provide a couple ways for constructing quasi-statistical and structures by means pseudo-Riemannian metric, an affine connection tensor field on smooth manifold, place these in relation with one another.

In this paper, we study generalized Douglas-Weyl Finsler metrics. We find some conditions under which the class of generalized Douglas-Weyl (&alpha, &beta)-metric with vanishing S-curvature reduce to the class of Berwald metrics.

We introduce a double complex that can be associated to certain Lie algebras, and show that its cohomology determines an obstruction to the existence of a half-flat SU(3)-structure. We obtain a classification of the 6-dimensional nilmanifolds carrying an invariant half-flat structure. MSC classification: Primary 53C25; Secondary 53C29, 17B30 An SU(3)-structure on a manifold of real dimension 6 ...

In this paper, we classify quasi-conformally flat generalized Sasakian-space forms under the assumption that characteristic vector field is Killing. Also Weyl-symmetric forms.

For k 2, we exhibit complete k-curvature homogeneous neutral signature pseudoRiemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous). All the local scalar Weyl invariants of these manifolds vanish. These manifolds are Ricci flat, Osserman, and Ivanov–Petrova. Mathematics Subject Classification (2000): 53B20.

This is a basically expository article tracing connections of the quantum potential to Fisher information, to Kähler geometry of the projective Hilbert space of a quantum system, and to the Weyl-Ricci scalar curvature of a Riemannian flat spacetime with quantum matter.

We show how the twisting of spectral triples induces a transition from Euclidean to Lorentzian noncommutative geometry at level fermionic action. More specifically, we compute action for closed manifold, then that two-sheet and finally triple electrodynamics in signature. obtain Weyl Dirac equations signature (and temporal gauge). The twisted is shown be invariant under an Lorentz group. This p...

We examine the boundary behaviour of the gauged N = (2, 0) supergravity in D = 3 coupled to an arbitrary number of scalar supermultiplets which parametrize a Kähler manifold. In addition to the gravitational coupling constant, the model depends on two parameters, namely the cosmological constant and the size of the Kähler manifold. It is shown that regular and irregular boundary conditions can ...