Related papers: Generalized Weierstrass-Enneper inducing, conforma…
A study of the generalized Weierstrass system which can be used to induce mean curvature surfaces in three-dimensional Euclidean space is presented.
Quasiclassical generalized Weierstrass representation (GWR) for highly corrugated surfaces with slow modulation in the four-dimensional Euclidean space is proposed. Integrable deformations of such surfaces are described by the…
Generalized geometry provides the framework for a systematic approach to non-symmetric metric gravity theory and naturally leads to an Einstein-Kalb-Ramond gravity theory with totally anti-symmetric contortion. The approach is related to…
We review the construction of generalized integrable hierarchies of partial differential equations, associated to affine Kac-Moody algebras, that include those considered by Drinfel'd and Sokolov. These hierarchies can be used to construct…
Embedding diagrams prove to be quite useful when learning general relativity as they offer a way of visualizing spacetime curvature through warped two dimensional (2D) surfaces. In this manuscript we present a different 2D construct that…
Several classes of solutions of the generalized Weierstrass system, which induces constant mean curvature surfaces into four-dimensional Euclidean space are constructed. A gauge transformation allows us to simplify the system considered and…
We introduce a class of generalized relative entropies (inspired by the Bregman divergence in information theory) on the Wasserstein space over a weighted Riemannian or Finsler manifold. We prove that the convexity of all the entropies in…
An alternative derivation of generalized gravitational entropy associated to co-dimension 2 'entangling' hypersurfaces is given. The approach is similar to the Jacobson-Myers 'Hamiltonian' method and it does not require computations on…
This paper refers to the study of generalized Struve type function. Using generalized Galue type Struve function (GTSF) by Nisar et al. [13], we derive various integral transform, including Euler transform, Laplace transform, Whittakar…
We study the approach to gravity in which our curved spacetime is considered as a surface in a flat ambient space of higher dimension (the embedding theory). The dynamical variable in this theory is not a metric but an embedding function.…
Weyl's conformal theory of gravity is an extension of Einstein's theory of general relativity which associates metrics with 1-forms . In the case of locally integrable (closed non-exact) 1-forms the spacetime manifolds are no more simply…
A brief review is given of an adaptation of the coadjoint orbit method appropriate for study of models with infinite-dimensional symmetry groups. It is illustrated on several examples, including derivation of the WZNW action of induced…
The interaction of matter with gravity in two dimensional spacetimes can be supplemented with a geometrical force analogous to a Lorentz force produced on a surface by a constant perpendicular magnetic field. In the special case of constant…
We study the gravitational action induced by coupling two-dimensional non-conformal, massive matter to gravity on a compact Riemann surface. We express this gravitational action in terms of finite and well-defined quantities for any value…
Recently, Chandrasekaran, Penington and Witten (CPW) have shown that the generalized entropy of the Schwarzschild black hole at the bifurcation surface equals the entropy of an extended von Neumann algebra of quantum observables in the…
A geometrical study of supergravity defined on (1|1) complex superspace is presented. This approach is based on the introduction of generalized superprojective structures extending the notions of super Riemann geometry to a kind of super…
The goal of the present paper is to investigate the algebraic structure of global conformal invariants of submanifolds. These are defined to be conformally invariant integrals of geometric scalars of the tangent and normal bundle. A famous…
The renormalization group flow in two--dimensional field theories that are coupled to gravity is discussed at the example of the sine-Gordon model. In order to derive the phase diagram in agreement with the matrix model results, it is…
We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…
Einstein-Weyl geometry is a triple (D,g,w), where D is a symmetric connection, [g] is a conformal structure and w is a covector such that: (i) connection D preserves the conformal class [g], that is, Dg=wg; (ii) trace-free part of the…