The propagation of Rossby waves on the Earth’s δ-surface is discussed in a reference frame propagation with the zonal phase speed of the wave.In this reference frame,trajectories and streamlines coincide;the propaga...The propagation of Rossby waves on the Earth’s δ-surface is discussed in a reference frame propagation with the zonal phase speed of the wave.In this reference frame,trajectories and streamlines coincide;the propagation of Rossby waves has a different interpretation than in a reference frame fixed on the ground;and the mechanism for the propagation of Rossby waves depends not only on the different positions of the wave relative to the basic current,but also the variation ofβwith latitude(called theδ-effect).展开更多
In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special （α, β）-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessa...In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special （α, β）-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessary condition that F is locally projectively fiat if and only if α and β satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively fiat. Moreover, we prove that such projectively fiat Finsler metrics with constant flag curvature must be locally Minkowskian.展开更多
In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential...In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential Finsler metric F is locally projectively flat if and only if α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of expo-nential Finsler metric F vanishes if and only if β is parallel with respect to α. And from this fact, we get that if exponential Finsler metric F is the Douglas metric, then F is not only a Berwald metric, but also a Landsberg metric.展开更多
基金supported by the National Natural Science Foundation of China [grant numbers 11362012,11562014,41465002,and 41765004]the High School Science Research Project of the Inner Mongolia Autonomous Region[grant number NJZY16096]the Natural Science Foundation of Inner Mongolia[grant number 2018LH04005]
文摘The propagation of Rossby waves on the Earth’s δ-surface is discussed in a reference frame propagation with the zonal phase speed of the wave.In this reference frame,trajectories and streamlines coincide;the propagation of Rossby waves has a different interpretation than in a reference frame fixed on the ground;and the mechanism for the propagation of Rossby waves depends not only on the different positions of the wave relative to the basic current,but also the variation ofβwith latitude(called theδ-effect).
基金Project (No. 10571154) supported by the National Natural Science Foundation of China
文摘In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special （α, β）-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessary condition that F is locally projectively fiat if and only if α and β satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively fiat. Moreover, we prove that such projectively fiat Finsler metrics with constant flag curvature must be locally Minkowskian.
基金Project (No. 10571154) supported by the National Natural ScienceFoundation of China
文摘In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential Finsler metric F is locally projectively flat if and only if α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of expo-nential Finsler metric F vanishes if and only if β is parallel with respect to α. And from this fact, we get that if exponential Finsler metric F is the Douglas metric, then F is not only a Berwald metric, but also a Landsberg metric.
