The Experts below are selected from a list of 21 Experts worldwide ranked by ideXlab platform
Amir Babak Aazami - One of the best experts on this subject based on the ideXlab platform.
-
The Newman-Penrose formalism for Riemannian 3-manifolds
Journal of Geometry and Physics, 2015Co-Authors: Amir Babak AazamiAbstract:Abstract We adapt the Newman–Penrose formalism in general relativity to the setting of three-dimensional Riemannian geometry, and prove the following results. Given a Riemannian 3-manifold without boundary and a smooth Unit Vector field k with geodesic flow, if an integral curve of k is hypersurface-Orthogonal at a point, then it is so at every point along that curve. Furthermore, if k is complete, hypersurface-Orthogonal, and satisfies Ric ( k , k ) ≥ 0 , then its divergence must be nonnegative. As an application, we show that if the Riemannian 3-manifold is closed and a Unit length k with geodesic flow satisfies Ric ( k , k ) > 0 , then k cannot be hypersurface-Orthogonal, thus recovering a result in Harris and Paternain (2013). Turning next to scalar curvature, we derive an evolution equation for the scalar curvature in terms of Unit Vector fields k that satisfy the condition R ( k , ⋅ , ⋅ , ⋅ ) = 0 . When the scalar curvature is a nonzero constant, we show that a hypersurface-Orthogonal Unit Vector field k satisfies R ( k , ⋅ , ⋅ , ⋅ ) = 0 if and only if it is a Killing Vector field.
-
The Newman-Penrose Formalism for Riemannian 3-manifolds
arXiv: Differential Geometry, 2014Co-Authors: Amir Babak AazamiAbstract:We adapt the Newman-Penrose formalism in general relativity to the setting of three-dimensional Riemannian geometry, and prove the following results. Given a Riemannian 3-manifold without boundary and a smooth Unit Vector field ${\boldsymbol k}$ with geodesic flow, if an integral curve of ${\boldsymbol k}$ is hypersurface-Orthogonal at a point, then it is so at every point along that curve. Furthermore, if ${\boldsymbol k}$ is complete, hypersurface-Orthogonal, and satisfies $\text{Ric}({\boldsymbol k},{\boldsymbol k}) \geq 0$, then its divergence must be nonnegative. As an application, we show that if the Riemannian 3-manifold is closed and a Unit length ${\boldsymbol k}$ with geodesic flow satisfies $\text{Ric}({\boldsymbol k},{\boldsymbol k}) > 0$, then ${\boldsymbol k}$ cannot be hypersurface-Orthogonal, thus recovering a recent result. Turning next to scalar curvature, we derive an evolution equation for the scalar curvature in terms of Unit Vector fields ${\boldsymbol k}$ that satisfy the condition $R({\boldsymbol k},\cdot,\cdot,\cdot) = 0$. When the scalar curvature is a nonzero constant, we show that a hypersurface-Orthogonal Unit Vector field ${\boldsymbol k}$ satisfies $R({\boldsymbol k},\cdot,\cdot,\cdot) = 0$ if and only if it is a Killing Vector field.
Münevver Yildirim Yilmaz - One of the best experts on this subject based on the ideXlab platform.
-
Some Local Expressions of Special Curves in Three Dimentional Finsler Manifold F3
Prespacetime Journal, 2015Co-Authors: Mihriban Külahcı, Münevver Yildirim YilmazAbstract:In the Euclidean space E 3 , there exist three classes of curves, so-called rectifying, normal and osculating curves satisfying the planes spanned by { T, B }, { N, B } and { T, N } as well as to each Unit speed curve I [ IR -> E 3 whose Orthogonal Unit Vector fields T, N, B called respectively the tangent, the principal normal and the binormal Vector fields. In this paper, we give the definition of rectifying, normal and osculating curves in 3-dimensional Finsler manifold. Furthermore, we obtain some characterizations related to these curves.
Mihriban Külahcı - One of the best experts on this subject based on the ideXlab platform.
-
Some Local Expressions of Special Curves in Three Dimentional Finsler Manifold F3
Prespacetime Journal, 2015Co-Authors: Mihriban Külahcı, Münevver Yildirim YilmazAbstract:In the Euclidean space E 3 , there exist three classes of curves, so-called rectifying, normal and osculating curves satisfying the planes spanned by { T, B }, { N, B } and { T, N } as well as to each Unit speed curve I [ IR -> E 3 whose Orthogonal Unit Vector fields T, N, B called respectively the tangent, the principal normal and the binormal Vector fields. In this paper, we give the definition of rectifying, normal and osculating curves in 3-dimensional Finsler manifold. Furthermore, we obtain some characterizations related to these curves.
An Qi Wang - One of the best experts on this subject based on the ideXlab platform.
-
Simulation of EM Scattering from 3-D Target by MOM with Pulse Basis Function
Advanced Materials Research, 2011Co-Authors: Yuan Ben Miao, An Qi WangAbstract:In this paper, electromagnetic (EM) scattering from a 3-D PEC target is simulated. The method of moments (MOM) with the pulse basis function and the point matching technique is presented to solve the magnetic field integral equation (MFIE). The flat triangular patch is applied to subdivide the surface of the 3-D target, and the surface unknowns are the arbitrary Orthogonal Unit Vector of the triangular patch. Validity of this algorithm is shown by comparing the E plane and H plane radar cross section (RCS) from a sphere or a cylinder to those results of MOM with the RWG Vector basis function. It is necessary to note that computational time of the algorithm presented in this paper is less than the MOM with the RWG(Rao Wilton Glisson) basis function.
Yuan Ben Miao - One of the best experts on this subject based on the ideXlab platform.
-
Simulation of EM Scattering from 3-D Target by MOM with Pulse Basis Function
Advanced Materials Research, 2011Co-Authors: Yuan Ben Miao, An Qi WangAbstract:In this paper, electromagnetic (EM) scattering from a 3-D PEC target is simulated. The method of moments (MOM) with the pulse basis function and the point matching technique is presented to solve the magnetic field integral equation (MFIE). The flat triangular patch is applied to subdivide the surface of the 3-D target, and the surface unknowns are the arbitrary Orthogonal Unit Vector of the triangular patch. Validity of this algorithm is shown by comparing the E plane and H plane radar cross section (RCS) from a sphere or a cylinder to those results of MOM with the RWG Vector basis function. It is necessary to note that computational time of the algorithm presented in this paper is less than the MOM with the RWG(Rao Wilton Glisson) basis function.
