Related papers: Surfaces with flat normal connection in 4-dimensio…
In a 4-manifold, the composition of a Riemannian Einstein metric with an almost paracomplex structure that is isometric and parallel, defines a neutral metric that is conformally flat and scalar flat. In this paper, we study hypersurfaces…
We investigate L-sectional curvature of S-manifolds with respect to the Rieman- nian connection and to certain semi-symmetric metric and non-metric connections naturally related with the structure, obtaining conditions for them to be…
We construct and investigate smooth orientable surfaces in su(N) algebras. The structural equations of surfaces associated with Grassmannian sigma models on Minkowski space are studied using moving frames adapted to the surfaces. The first…
In this work, we consider spacelike surfaces in Minkowski space $\hbox{\bf E}%_{1}^{3}$ that satisfy a linear Weingarten condition of type $\kappa_{1}=m\kappa_{2}+n$, where $m$ and $n$ are constant and $\kappa_{1}$ and $\kappa_{2}$ denote…
SU(2) flat connection on 2D Riemann surface is shown to relate to the generalized twisted geometry in 3D space with cosmological constant. Various flat connection quantities on Riemann surface are mapped to the geometrical quantities in…
In this paper I consider surfaces in a space-time with a Killing vector $\xi^{\alpha}$ that is time-like and hypersurface orthogonal on one side of the surface. The Killing vector may be either time-like or space-like on the other side of…
In this article a relation between curvature functionals for surfaces in the Euclidean space and area functionals in relative differential geometry will be given. Relative differential geometry can be described as the geometry of surfaces…
We review part of the classical theory of curves and surfaces in $3$-dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.
The purpose of this article is to determine explicitly the complete surfaces with parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane. The main results are as follows: When the curvature of…
We apply the complex analysis over the double numbers $D$ to study the minimal time-like surfaces in $R^4_2$. A minimal time-like surface which is free of degenerate points is said to be of general type. We divide the minimal time-like…
Lagrangian curves in 4-space entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic…
For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework…
We classify rotational surfaces in a normed 3-space with rotationally symmetric norm whose principal curvatures satisfy a linear relation.
We propose that the phases of all vicinal surfaces can be characterized by four fixed lines, in the renormalization group sense, in a three-dimensional space of coupling constants. The observed configurations of several Si surfaces are…
A zero mean curvature surface in the Lorentz-Minkowski 3-space is said to be of Riemann-type if it is foliated by circles and at most countably many straight lines in parallel planes. We classify all zero mean curvature surfaces of…
We study surfaces in $\R^4$ whose tangent spaces have constant principal angles with respect to a plane. Using a PDE we prove the existence of surfaces with arbitrary constant principal angles. The existence of such surfaces turns out to be…
We extend the methods of Davis-Januszkiewicz-Lafont to provide a new obstruction to smooth Riemannian metric with non-positive sectional curvature. We construct examples of locally CAT(0) 4-manifolds $M$, whose universal covers satisfy…
We study surfaces with parallel normalized mean curvature vector field in Euclidean or Minkowski 4-space. On any such surface we introduce special isothermal parameters (canonical parameters) and describe these surfaces in terms of three…
This review examines the role of differential forms, Pfaffian systems, and hypersurfaces in general relativity. These mathematical constructions provide the essential tools for general relativity, in which the curvature of…
Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in $S^4$, are studied in this paper. We define two kinds of transforms for such a…