جستجوی مقالات مرتبط با کلیدواژه « riemannian metric » در نشریات گروه « ریاضی »
تکرار جستجوی کلیدواژه «riemannian metric» در نشریات گروه «علوم پایه»-
In the present paper, we compute the conservation laws of the Vaidya-Bonner geodesic space-time metric in aRiemannian space and carry out the moving frame method for this metric. We obtain the connection forms andcurvature 2-forms, using the first and second Cartan's structure equations. Finally, the Ricci scalar tensor and the components of Einstein curvature are calculated.
Keywords: Conservation laws, Geodesic, Riemannian metric, Moving frame} -
In this paper, we use the mean curvature flow PDE and geodesic ODE to smooth and trace evolving curves as boundaries of minimal surfaces for a gray-scale image to capture their boundaries.Keywords: Geodesic, image processing, minimal surface, mean curvature, Riemannian metric}
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On a real vector space V , a Randers norm Fˆ is defined by Fˆ = ˆα+βˆ, where ˆα is a Euclidean norm and βˆ is a covector. We show that the unit sphere Σ in the Randers space (V, Fˆ) has positive flag curvature, if and only if |βˆ|αˆ < (5 − √ 17)/2 ≈ 0.43845, thus answering a problem proposed by Prof. Zhongmin Shen. Moreover, we prove that the flag curvature of Σ has a universal lower bound −4.Keywords: flag curvature, Randers Metric, Riemannian metric}
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In this paper, using a map on the product space, we define a linear functional on a Hilbert space and we extract the metric entropy of a system as the operator norm of the linear functional. This follows an approach which considers the entropy of a dynamical system as a linear operator.Keywords: Dynamical system, entropy, Riemannian metric}
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In this article, we study the algebraic Ricci solitons of three-dimensional Lie group $mathbb{H}^{2}timesmathbb{R}$, endowed with a left-invariant Riemannian metric. Also, we examine the existence of sol-solitons on the three-dimensional Lie group $Sol_{3}$, endowed with a left-invariant Riemannian metric.
Keywords: Algebraic Ricci soliton, Lie group, Riemannian metric} -
In this paper, we give a classification of left-invariant Douglas and Berwald $(alpha,beta)$-metrics on simply connected four-dimensional nilpotent Lie groups. We show that there are not any bi-invariant Randers metrics on four-dimensional nilpotent Lie groups. Then, we explicitly give the flag curvature formulas and geodesic vectors of these spaces. Finally, we give the formula of $S$-curvature of left-invariant Randers metrics of Douglas type.
Keywords: nilpotent Lie group, Riemannian metric, $(alpha, beta)$-metric, flag curvature}
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