Steady States for One Dimensional Conformal Metric Flows
نویسندگان
چکیده
We define two conformal structures on S which give rise to a different view of the affine curvature flow and a new curvature flow, the “Qcurvature flow”. The steady state of these flows are studied. More specifically, we prove four sharp inequalities, which state the existences of the corresponding extremal metrics.
منابع مشابه
N ov 2 00 6 ONE DIMENSIONAL CONFORMAL METRIC FLOWS
In this paper we continue our studies of the one dimensional conformal metric flows, which were introduced in [9]. We prove the global existence and convergence of the flows, as well as the exponential convergence of the metrics under these flows.
متن کاملOn Infinitesimal Conformal Transformations of the Tangent Bundles with the Generalized Metric
Let be an n-dimensional Riemannian manifold, and be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation induces an infinitesimal homothetic transformation on . Furthermore, the correspondence gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on onto the Lie algebra of infinitesimal ...
متن کاملar X iv : 0 71 0 . 43 17 v 1 [ m at h . A P ] 2 3 O ct 2 00 7 ONE DIMENSIONAL CONFORMAL METRIC FLOW II
In this paper we continue our studies of the one dimensional conformal metric flows, which were introduced in [8]. In this part we mainly focus on evolution equations involving fourth order derivatives. The global existence and exponential convergence of metrics for the 1-Q and 4-Q flows are obtained.
متن کاملSimulation of Ideal External and Internal Flows with Arbitrary Boundaries Using Schwarz Christoffel Transformation
The flow field, velocity and pressure coefficient distribution of some 2-D ideal flows are presented. Conformal mapping is used to simulate two-dimensional ideal flow for a variety of complex internal and external configurations, based on the numerical integration of Schwarz-Christoffel transformation. The advantages of this method are simplicity and high accuracy. The method presented in this ...
متن کاملCalculation of the relativistic bulk tensor and shear tensor of relativistic accretion flows in the Kerr metric.
In this paper, we calculate the relativistic bulk tensor and shear tensor of the relativistic accretion ows in the Kerr metric, overall and without any approximation. We obtain the relations of all components of the relativistic bulk and shear tensor in terms of components of four-velocity and its derivatives, Christoffel symbols and metric components in the BLF. Then, these components are deri...
متن کامل