We introduce a two-dimensional frustrated Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. Classically the two sublattices decouple, and "order from disorder" drives them into a coplanar state. Applying Friedan's geometric approach to nonlinear sigma models, we obtain the scaling of the spin stiffnesses governed by the Ricci flow of a four-dimensional metric ten...

2+1-dimensional Yang-Mills theory is reinterpreted in terms of metrics on 3manifolds. The dual gluons are related to diffeomorphisms of the 3-manifolds. Monopoles are identified with points where the Ricci tensor has triply degenerate eigenvalues. The dual gluons have the desired interaction with these monopoles. This would give a mass for the dual gluons resulting in confinement. PACS No.(s) 1...

According to a classical result of E. Calabi any hyperbolic affine hypersphere endowed with its natural Hessian metric has a non-positive Ricci tensor. The affine hyperspheres can be described as the level sets of solutions to the “hyperbolic” toric Kähler-Einstein equation e = detDΦ on proper convex cones. We prove a generalization of this theorem showing that for every Φ solving this equation...

We study symplectic manifolds (M, ω) equipped with a symplectic torsion-free affine (also called Fedosov) connection ∇ and admitting a metaplectic structure. Let S be the so called symplectic spinor bundle and let R be the curvature tensor field of the symplectic spinor covariant derivative ∇ associated to the Fedosov connection ∇. It is known that the space of symplectic spinor valued exterior...

Recently, Amendola et al. proposed a geometrical theory of gravity containing higher-order derivative terms. The authors introduced anticurvature scalar $(A)$, which is the trace inverse Ricci tensor ($A^{\mu\nu} = R_{\mu\nu}^{-1}$). In this work, we consider two classes Ricci-inverse -- Class I and II models. models are form $f(R, A)$ where $f$ function scalars. ${\cal F}(R, A^{\mu\nu}A_{\mu\n...

The paper undertakes certain special forms of the quarter symmetric metric and non-metric connections on an ε-anti-Kähler manifold. Firstly, we deduce relation between Riemannian connection connections. Then, present some results concerning torsion tensors these In addition, find curvature tensor, Ricci tensor scalar such search conditions for manifold to be Einstein space with respect Finally,...