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Geodesic connectedness of a spacetime with a causal Killing vector field. [PDF]

We study the geodesic connectedness of a globally hyperbolic spacetime (M, g) admitting a complete smooth Cauchy hypersurface S and endowed with a complete causal Killing vector field K. The main assumptions are that the kernel distribution D of the one-form induced by K on S is non-integrable and that the gradient of g(K, K) is orthogonal to D.
Bartolo, Rossella
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On geodesibility of algebrizable planar vector fields

Boletín de la Sociedad Matemática Mexicana, 2017
The authors consider an algebra \(\mathbb{A}\) as the space \(\mathbb{R}^2\) endowed with a structure of associative, commutative algebra with unit, denoted by \(e\). Three parametric families of non-isomorphic algebras are considered, in particular the algebra of the complex numbers \(\mathbb{C}\) appears. A vector field \(F : \Omega \subset \mathbb{R}
M. E. Frías-Armenta, E. López-González   +1 more
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Gradient vector flow fast geodesic active contours

Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001, 2002
This paper proposes a new front propagation flow for boundary extraction. The proposed framework is inspired by the geodesic active contour model and leads to a paradigm that is relatively free from the initial curve position. Towards this end, it makes use of a recently introduced external boundary force, the gradient vector field that refers to a ...
Nikos Paragios, Olivier Mellina-Gottardo, Visvanathan Ramesh   +2 more
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Geodesic mappings of spaces with φ(Ric) vector fields

AIP Conference Proceedings, 2020
The paper treats a special type of pseudo-Riemannian spaces, namely those which permit φ(Ric)-vector fields. These spaces are widely applied in mechanics and relativity theory. Authors demonstrated a shape taken by a linear form of basic equations of theory of geodesic mappings for the above-mentioned spaces. These equations take a shape of a system of
Y. Vashpanov, O. Olshevska, O. Lesechko
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Geodesics and Parallelism of Vectors

2016
The shortest distance between two points located on a surface of the Riemann space E N is related to a curve of stationary value, which equation is obtained by means of the variational calculus. This curve is called geodesic. The checking of the existence of this type of curve is carried out from the basic concepts of the elementary geometry.
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Curved Phenine Normal Vectors: Geometric Measures of Geodesic Phenine Frameworks

Chemistry – An Asian Journal, 2020
AbstractA vector was introduced to quantitatively describe the pyramidalization of 1,3,5‐trisubstituted benzene (phenine). The vector, named curved phenine normal vector (CPNV), defined the direction of pyramidalization of the trigonal phenine panel and quantified the degree of pyramidalization. The relative orientation of the two CPNVs further defined
Tatsuru Mio, Koki Ikemoto, Hiroyuki Isobe   +2 more
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On geodesible vector fields and related geometric structures [PDF]

, 2023
A nowhere vanishing vector field X on a manifold M is called geodesible if there exists a Riemannian metric on M for which X is of unit length and such that the orbits of X are geodesics. After discussing some examples of such vector fields, we extend an existence result of Gluck and Hajduk--Walczak about geodesible vector fields on odd-dimensional ...
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Existence and uniqueness results for the gradient vector flow and geodesic active contours mixed model

Communications on Pure and Applied Analysis, 2009
International audienceThis article deals with the so called GVF (Gradient Vector Flow) introduced by C. Xu, J.L. Prince . We give existence and uniqueness results for the front propagation flow for boundary extraction that was initiated by Paragios ...
Bergounioux, Maïtine, Guillot, Laurence
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Geodesic Vector fields of invariant $(α,β)$-metrics on Homogeneous spaces

2012
In this paper we show that for an invariant $(α,β)-$metric $F$ on a homogeneous Finsler manifold $\frac{G}{H}$, induced by an invariant Riemannian metric $\tilde{a}$ and an invariant vector field $\tilde{X}$, the vector $X=\tilde{X}(H)$ is a geodesic vector of $F$ if and only if it is a geodesic vector of $\tilde{a}$.
PARHIZKAR, M., MOGHADDAM, H. R. Salimi
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Geodesibility of algebrizable three-dimensional vector fields

Abstract. For each algebrizable three-dimensional vector field F, in this paper we give local rectifications Hα of F, which let us to show that F is geodesible with respect to the Riemannian metric g. Furthermore, an orthonormal frame {E1,E2,E3} for g, where Ei = eiF and {e1,e2,e3} is the canonical basis of R3.
Julio Cesar Avila, Martín-Eduardo Frias-Armenta, Elifalet López-González   +2 more
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